GCSE Maths: Equations with brackets (Foundation)

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(x + 3) = 14
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(x + 3):
   2 × x = 2x
   2 × 3 = 6
   
   The equation is now 2x + 6 = 14
3. Subtract 6 from both sides. This undoes the +6, because +6 − 6 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x + 6 − 6 = 14 − 6
   2x = 8
4. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 82
   x = 82 = 4
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 4

Check. Substitute x = 4 into the original equation. Left side: 2 × (4 + 3) = 2 × 7 = 14. Right side: 14. Both sides equal 14, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(x + 1) = 18
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(x + 1):
   3 × x = 3x
   3 × 1 = 3
   
   The equation is now 3x + 3 = 18
3. Subtract 3 from both sides. This undoes the +3, because +3 − 3 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   3x + 3 − 3 = 18 − 3
   3x = 15
4. Divide both sides by 3. 3x means 3 multiplied by x. The inverse of multiplying by 3 is dividing by 3, and we do it to both sides to keep the balance. This leaves x on its own.
   3x3 = 153
   x = 153 = 5
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 3 × (5 + 1) = 3 × 6 = 18. Right side: 18. Both sides equal 18, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   5(x + 2) = 35
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 5(x + 2):
   5 × x = 5x
   5 × 2 = 10
   
   The equation is now 5x + 10 = 35
3. Subtract 10 from both sides. This undoes the +10, because +10 − 10 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   5x + 10 − 10 = 35 − 10
   5x = 25
4. Divide both sides by 5. 5x means 5 multiplied by x. The inverse of multiplying by 5 is dividing by 5, and we do it to both sides to keep the balance. This leaves x on its own.
   5x5 = 255
   x = 255 = 5
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 5 × (5 + 2) = 5 × 7 = 35. Right side: 35. Both sides equal 35, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   4(x + 5) = 36
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 4(x + 5):
   4 × x = 4x
   4 × 5 = 20
   
   The equation is now 4x + 20 = 36
3. Subtract 20 from both sides. This undoes the +20, because +20 − 20 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   4x + 20 − 20 = 36 − 20
   4x = 16
4. Divide both sides by 4. 4x means 4 multiplied by x. The inverse of multiplying by 4 is dividing by 4, and we do it to both sides to keep the balance. This leaves x on its own.
   4x4 = 164
   x = 164 = 4
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 4

Check. Substitute x = 4 into the original equation. Left side: 4 × (4 + 5) = 4 × 9 = 36. Right side: 36. Both sides equal 36, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   6(x + 1) = 30
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 6(x + 1):
   6 × x = 6x
   6 × 1 = 6
   
   The equation is now 6x + 6 = 30
3. Subtract 6 from both sides. This undoes the +6, because +6 − 6 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   6x + 6 − 6 = 30 − 6
   6x = 24
4. Divide both sides by 6. 6x means 6 multiplied by x. The inverse of multiplying by 6 is dividing by 6, and we do it to both sides to keep the balance. This leaves x on its own.
   6x6 = 246
   x = 246 = 4
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 4

Check. Substitute x = 4 into the original equation. Left side: 6 × (4 + 1) = 6 × 5 = 30. Right side: 30. Both sides equal 30, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(x + 9) = 30
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(x + 9):
   2 × x = 2x
   2 × 9 = 18
   
   The equation is now 2x + 18 = 30
3. Subtract 18 from both sides. This undoes the +18, because +18 − 18 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x + 18 − 18 = 30 − 18
   2x = 12
4. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 122
   x = 122 = 6
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 6

Check. Substitute x = 6 into the original equation. Left side: 2 × (6 + 9) = 2 × 15 = 30. Right side: 30. Both sides equal 30, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(x − 2) = 15
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(x − 2):
   3 × x = 3x
   3 × (−2) = −6
   
   The equation is now 3x − 6 = 15
3. Add 6 to both sides. This undoes the −6, because −6 + 6 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   3x − 6 + 6 = 15 + 6
   3x = 21
4. Divide both sides by 3. 3x means 3 multiplied by x. The inverse of multiplying by 3 is dividing by 3, and we do it to both sides to keep the balance. This leaves x on its own.
   3x3 = 213
   x = 213 = 7
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 7

Check. Substitute x = 7 into the original equation. Left side: 3 × (7 − 2) = 3 × 5 = 15. Right side: 15. Both sides equal 15, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(x − 4) = 10
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(x − 4):
   2 × x = 2x
   2 × (−4) = −8
   
   The equation is now 2x − 8 = 10
3. Add 8 to both sides. This undoes the −8, because −8 + 8 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x − 8 + 8 = 10 + 8
   2x = 18
4. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 182
   x = 182 = 9
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 9

Check. Substitute x = 9 into the original equation. Left side: 2 × (9 − 4) = 2 × 5 = 10. Right side: 10. Both sides equal 10, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   5(x − 1) = 20
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 5(x − 1):
   5 × x = 5x
   5 × (−1) = −5
   
   The equation is now 5x − 5 = 20
3. Add 5 to both sides. This undoes the −5, because −5 + 5 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   5x − 5 + 5 = 20 + 5
   5x = 25
4. Divide both sides by 5. 5x means 5 multiplied by x. The inverse of multiplying by 5 is dividing by 5, and we do it to both sides to keep the balance. This leaves x on its own.
   5x5 = 255
   x = 255 = 5
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 5 × (5 − 1) = 5 × 4 = 20. Right side: 20. Both sides equal 20, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   4(x − 3) = 8
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 4(x − 3):
   4 × x = 4x
   4 × (−3) = −12
   
   The equation is now 4x − 12 = 8
3. Add 12 to both sides. This undoes the −12, because −12 + 12 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   4x − 12 + 12 = 8 + 12
   4x = 20
4. Divide both sides by 4. 4x means 4 multiplied by x. The inverse of multiplying by 4 is dividing by 4, and we do it to both sides to keep the balance. This leaves x on its own.
   4x4 = 204
   x = 204 = 5
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 4 × (5 − 3) = 4 × 2 = 8. Right side: 8. Both sides equal 8, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(2x + 1) = 21
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(2x + 1):
   3 × 2x = 6x
   3 × 1 = 3
   
   The equation is now 6x + 3 = 21
3. Subtract 3 from both sides. This undoes the +3, because +3 − 3 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   6x + 3 − 3 = 21 − 3
   6x = 18
4. Divide both sides by 6. 6x means 6 multiplied by x. The inverse of multiplying by 6 is dividing by 6, and we do it to both sides to keep the balance. This leaves x on its own.
   6x6 = 186
   x = 186 = 3
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 3 × (2 × 3 + 1) = 3 × 7 = 21. Right side: 21. Both sides equal 21, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(3x − 4) = 22
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(3x − 4):
   2 × 3x = 6x
   2 × (−4) = −8
   
   The equation is now 6x − 8 = 22
3. Add 8 to both sides. This undoes the −8, because −8 + 8 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   6x − 8 + 8 = 22 + 8
   6x = 30
4. Divide both sides by 6. 6x means 6 multiplied by x. The inverse of multiplying by 6 is dividing by 6, and we do it to both sides to keep the balance. This leaves x on its own.
   6x6 = 306
   x = 306 = 5
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 2 × (3 × 5 − 4) = 2 × 11 = 22. Right side: 22. Both sides equal 22, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(x + 2) + 4 = 19
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(x + 2):
   3 × x = 3x
   3 × 2 = 6
   
   The equation is now 3x + 6 + 4 = 19
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 6 + 4 make 10.
   The equation is now 3x + 10 = 19
4. Subtract 10 from both sides. This undoes the +10, because +10 − 10 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   3x + 10 − 10 = 19 − 10
   3x = 9
5. Divide both sides by 3. 3x means 3 multiplied by x. The inverse of multiplying by 3 is dividing by 3, and we do it to both sides to keep the balance. This leaves x on its own.
   3x3 = 93
   x = 93 = 3
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 3 × (3 + 2) + 4 = 3 × 5 + 4 = 15 + 4 = 19. Right side: 19. Both sides equal 19, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(x + 5) − 3 = 19
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(x + 5):
   2 × x = 2x
   2 × 5 = 10
   
   The equation is now 2x + 10 − 3 = 19
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 10 − 3 make 7.
   The equation is now 2x + 7 = 19
4. Subtract 7 from both sides. This undoes the +7, because +7 − 7 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x + 7 − 7 = 19 − 7
   2x = 12
5. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 122
   x = 122 = 6
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 6

Check. Substitute x = 6 into the original equation. Left side: 2 × (6 + 5) − 3 = 2 × 11 − 3 = 22 − 3 = 19. Right side: 19. Both sides equal 19, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   4(x − 1) + 7 = 23
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 4(x − 1):
   4 × x = 4x
   4 × (−1) = −4
   
   The equation is now 4x − 4 + 7 = 23
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers −4 + 7 make 3.
   The equation is now 4x + 3 = 23
4. Subtract 3 from both sides. This undoes the +3, because +3 − 3 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   4x + 3 − 3 = 23 − 3
   4x = 20
5. Divide both sides by 4. 4x means 4 multiplied by x. The inverse of multiplying by 4 is dividing by 4, and we do it to both sides to keep the balance. This leaves x on its own.
   4x4 = 204
   x = 204 = 5
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 4 × (5 − 1) + 7 = 4 × 4 + 7 = 16 + 7 = 23. Right side: 23. Both sides equal 23, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   5(x + 2) − 8 = 27
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 5(x + 2):
   5 × x = 5x
   5 × 2 = 10
   
   The equation is now 5x + 10 − 8 = 27
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 10 − 8 make 2.
   The equation is now 5x + 2 = 27
4. Subtract 2 from both sides. This undoes the +2, because +2 − 2 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   5x + 2 − 2 = 27 − 2
   5x = 25
5. Divide both sides by 5. 5x means 5 multiplied by x. The inverse of multiplying by 5 is dividing by 5, and we do it to both sides to keep the balance. This leaves x on its own.
   5x5 = 255
   x = 255 = 5
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 5 × (5 + 2) − 8 = 5 × 7 − 8 = 35 − 8 = 27. Right side: 27. Both sides equal 27, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(2x + 1) + 5 = 19
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(2x + 1):
   2 × 2x = 4x
   2 × 1 = 2
   
   The equation is now 4x + 2 + 5 = 19
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 2 + 5 make 7.
   The equation is now 4x + 7 = 19
4. Subtract 7 from both sides. This undoes the +7, because +7 − 7 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   4x + 7 − 7 = 19 − 7
   4x = 12
5. Divide both sides by 4. 4x means 4 multiplied by x. The inverse of multiplying by 4 is dividing by 4, and we do it to both sides to keep the balance. This leaves x on its own.
   4x4 = 124
   x = 124 = 3
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 2 × (2 × 3 + 1) + 5 = 2 × 7 + 5 = 14 + 5 = 19. Right side: 19. Both sides equal 19, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(x − 4) + 2 = 8
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(x − 4):
   3 × x = 3x
   3 × (−4) = −12
   
   The equation is now 3x − 12 + 2 = 8
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers −12 + 2 make −10.
   The equation is now 3x − 10 = 8
4. Add 10 to both sides. This undoes the −10, because −10 + 10 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   3x − 10 + 10 = 8 + 10
   3x = 18
5. Divide both sides by 3. 3x means 3 multiplied by x. The inverse of multiplying by 3 is dividing by 3, and we do it to both sides to keep the balance. This leaves x on its own.
   3x3 = 183
   x = 183 = 6
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 6

Check. Substitute x = 6 into the original equation. Left side: 3 × (6 − 4) + 2 = 3 × 2 + 2 = 6 + 2 = 8. Right side: 8. Both sides equal 8, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(x + 2) = 2x + 9
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(x + 2):
   3 × x = 3x
   3 × 2 = 6
   
   The equation is now 3x + 6 = 2x + 9
3. Remove the x term from the right side: subtract 2x from both sides. We want all the x terms on one side. The right side has 2x; subtracting 2x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   3x + 6 − 2x = 2x + 9 − 2x
   x + 6 = 9
4. Subtract 6 from both sides. This undoes the +6, because +6 − 6 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   x + 6 − 6 = 9 − 6
   x = 3
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 3 × (3 + 2) = 3 × 5 = 15. Right side: 2 × 3 + 9 = 6 + 9 = 15. Both sides equal 15, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   4(x − 1) = 2x + 8
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 4(x − 1):
   4 × x = 4x
   4 × (−1) = −4
   
   The equation is now 4x − 4 = 2x + 8
3. Remove the x term from the right side: subtract 2x from both sides. We want all the x terms on one side. The right side has 2x; subtracting 2x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   4x − 4 − 2x = 2x + 8 − 2x
   2x − 4 = 8
4. Add 4 to both sides. This undoes the −4, because −4 + 4 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x − 4 + 4 = 8 + 4
   2x = 12
5. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 122
   x = 122 = 6
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 6

Check. Substitute x = 6 into the original equation. Left side: 4 × (6 − 1) = 4 × 5 = 20. Right side: 2 × 6 + 8 = 12 + 8 = 20. Both sides equal 20, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(x + 5) = x + 14
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(x + 5):
   2 × x = 2x
   2 × 5 = 10
   
   The equation is now 2x + 10 = x + 14
3. Remove the x term from the right side: subtract x from both sides. We want all the x terms on one side. The right side has x; subtracting x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   2x + 10 − x = x + 14 − x
   x + 10 = 14
4. Subtract 10 from both sides. This undoes the +10, because +10 − 10 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   x + 10 − 10 = 14 − 10
   x = 4
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 4

Check. Substitute x = 4 into the original equation. Left side: 2 × (4 + 5) = 2 × 9 = 18. Right side: 4 + 14 = 18. Both sides equal 18, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   5(x − 3) = 3x + 1
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 5(x − 3):
   5 × x = 5x
   5 × (−3) = −15
   
   The equation is now 5x − 15 = 3x + 1
3. Remove the x term from the right side: subtract 3x from both sides. We want all the x terms on one side. The right side has 3x; subtracting 3x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   5x − 15 − 3x = 3x + 1 − 3x
   2x − 15 = 1
4. Add 15 to both sides. This undoes the −15, because −15 + 15 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x − 15 + 15 = 1 + 15
   2x = 16
5. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 162
   x = 162 = 8
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 8

Check. Substitute x = 8 into the original equation. Left side: 5 × (8 − 3) = 5 × 5 = 25. Right side: 3 × 8 + 1 = 24 + 1 = 25. Both sides equal 25, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(2x + 1) = 4x + 11
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(2x + 1):
   3 × 2x = 6x
   3 × 1 = 3
   
   The equation is now 6x + 3 = 4x + 11
3. Remove the x term from the right side: subtract 4x from both sides. We want all the x terms on one side. The right side has 4x; subtracting 4x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   6x + 3 − 4x = 4x + 11 − 4x
   2x + 3 = 11
4. Subtract 3 from both sides. This undoes the +3, because +3 − 3 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x + 3 − 3 = 11 − 3
   2x = 8
5. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 82
   x = 82 = 4
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 4

Check. Substitute x = 4 into the original equation. Left side: 3 × (2 × 4 + 1) = 3 × 9 = 27. Right side: 4 × 4 + 11 = 16 + 11 = 27. Both sides equal 27, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(3x − 2) = 5x + 3
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(3x − 2):
   2 × 3x = 6x
   2 × (−2) = −4
   
   The equation is now 6x − 4 = 5x + 3
3. Remove the x term from the right side: subtract 5x from both sides. We want all the x terms on one side. The right side has 5x; subtracting 5x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   6x − 4 − 5x = 5x + 3 − 5x
   x − 4 = 3
4. Add 4 to both sides. This undoes the −4, because −4 + 4 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   x − 4 + 4 = 3 + 4
   x = 7
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 7

Check. Substitute x = 7 into the original equation. Left side: 2 × (3 × 7 − 2) = 2 × 19 = 38. Right side: 5 × 7 + 3 = 35 + 3 = 38. Both sides equal 38, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   5(x − 2) = 3(x + 4)
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 5(x − 2):
   5 × x = 5x
   5 × (−2) = −10
   
   Expand 3(x + 4):
   3 × x = 3x
   3 × 4 = 12
   
   The equation is now 5x − 10 = 3x + 12
3. Remove the x term from the right side: subtract 3x from both sides. We want all the x terms on one side. The right side has 3x; subtracting 3x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   5x − 10 − 3x = 3x + 12 − 3x
   2x − 10 = 12
4. Add 10 to both sides. This undoes the −10, because −10 + 10 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x − 10 + 10 = 12 + 10
   2x = 22
5. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 222
   x = 222 = 11
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 11

Check. Substitute x = 11 into the original equation. Left side: 5 × (11 − 2) = 5 × 9 = 45. Right side: 3 × (11 + 4) = 3 × 15 = 45. Both sides equal 45, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(x + 7) = 4(x + 1)
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(x + 7):
   2 × x = 2x
   2 × 7 = 14
   
   Expand 4(x + 1):
   4 × x = 4x
   4 × 1 = 4
   
   The equation is now 2x + 14 = 4x + 4
3. Remove the x term from the left side: subtract 2x from both sides. We want all the x terms on one side. The left side has 2x; subtracting 2x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   2x + 14 − 2x = 4x + 4 − 2x
   14 = 2x + 4
4. Subtract 4 from both sides. This undoes the +4, because +4 − 4 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   14 − 4 = 2x + 4 − 4
   10 = 2x
5. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   102 = 2x2
   x = 102 = 5
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 2 × (5 + 7) = 2 × 12 = 24. Right side: 4 × (5 + 1) = 4 × 6 = 24. Both sides equal 24, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   4(x − 1) = 3(x + 2)
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 4(x − 1):
   4 × x = 4x
   4 × (−1) = −4
   
   Expand 3(x + 2):
   3 × x = 3x
   3 × 2 = 6
   
   The equation is now 4x − 4 = 3x + 6
3. Remove the x term from the right side: subtract 3x from both sides. We want all the x terms on one side. The right side has 3x; subtracting 3x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   4x − 4 − 3x = 3x + 6 − 3x
   x − 4 = 6
4. Add 4 to both sides. This undoes the −4, because −4 + 4 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   x − 4 + 4 = 6 + 4
   x = 10
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 10

Check. Substitute x = 10 into the original equation. Left side: 4 × (10 − 1) = 4 × 9 = 36. Right side: 3 × (10 + 2) = 3 × 12 = 36. Both sides equal 36, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   4(x + 3) = 3(x + 6)
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 4(x + 3):
   4 × x = 4x
   4 × 3 = 12
   
   Expand 3(x + 6):
   3 × x = 3x
   3 × 6 = 18
   
   The equation is now 4x + 12 = 3x + 18
3. Remove the x term from the right side: subtract 3x from both sides. We want all the x terms on one side. The right side has 3x; subtracting 3x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   4x + 12 − 3x = 3x + 18 − 3x
   x + 12 = 18
4. Subtract 12 from both sides. This undoes the +12, because +12 − 12 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   x + 12 − 12 = 18 − 12
   x = 6
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 6

Check. Substitute x = 6 into the original equation. Left side: 4 × (6 + 3) = 4 × 9 = 36. Right side: 3 × (6 + 6) = 3 × 12 = 36. Both sides equal 36, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   6(x − 2) = 2(x + 8)
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 6(x − 2):
   6 × x = 6x
   6 × (−2) = −12
   
   Expand 2(x + 8):
   2 × x = 2x
   2 × 8 = 16
   
   The equation is now 6x − 12 = 2x + 16
3. Remove the x term from the right side: subtract 2x from both sides. We want all the x terms on one side. The right side has 2x; subtracting 2x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   6x − 12 − 2x = 2x + 16 − 2x
   4x − 12 = 16
4. Add 12 to both sides. This undoes the −12, because −12 + 12 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   4x − 12 + 12 = 16 + 12
   4x = 28
5. Divide both sides by 4. 4x means 4 multiplied by x. The inverse of multiplying by 4 is dividing by 4, and we do it to both sides to keep the balance. This leaves x on its own.
   4x4 = 284
   x = 284 = 7
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 7

Check. Substitute x = 7 into the original equation. Left side: 6 × (7 − 2) = 6 × 5 = 30. Right side: 2 × (7 + 8) = 2 × 15 = 30. Both sides equal 30, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   5(2x − 1) = 3(3x + 1)
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 5(2x − 1):
   5 × 2x = 10x
   5 × (−1) = −5
   
   Expand 3(3x + 1):
   3 × 3x = 9x
   3 × 1 = 3
   
   The equation is now 10x − 5 = 9x + 3
3. Remove the x term from the right side: subtract 9x from both sides. We want all the x terms on one side. The right side has 9x; subtracting 9x removes it. We take away the smaller x term, so that the x term that is left is positive and easier to work with. We must do it to both sides to keep the balance.
   10x − 5 − 9x = 9x + 3 − 9x
   x − 5 = 3
4. Add 5 to both sides. This undoes the −5, because −5 + 5 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   x − 5 + 5 = 3 + 5
   x = 8
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 8

Check. Substitute x = 8 into the original equation. Left side: 5 × (2 × 8 − 1) = 5 × 15 = 75. Right side: 3 × (3 × 8 + 1) = 3 × 25 = 75. Both sides equal 75, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   10 − (x + 2) = 5
2. Expand the brackets. Multiply each term inside the bracket by the number outside it. A negative number multiplied by a negative number gives a positive answer, and a negative multiplied by a positive gives a negative.
   Expand −(x + 2):
   (−1) × x = −x
   (−1) × 2 = −2
   
   The equation is now 10 − x − 2 = 5
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 10 − 2 make 8.
   The equation is now −x + 8 = 5
4. Subtract 8 from both sides. This undoes the +8, because +8 − 8 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   −x + 8 − 8 = 5 − 8
   −x = −3
5. Divide both sides by −1. −x means −1 multiplied by x. The inverse of multiplying by −1 is dividing by −1, and we do it to both sides to keep the balance. This leaves x on its own. Careful with signs: a positive divided by a negative gives a negative answer, and a negative divided by a negative gives a positive.
   −x−1 = −3−1
   x = −3−1 = 3
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 10 − (3 + 2) = 10 − 5 = 5. Right side: 5. Both sides equal 5, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   7 − 2(x − 1) = 3
2. Expand the brackets. Multiply each term inside the bracket by the number outside it. A negative number multiplied by a negative number gives a positive answer, and a negative multiplied by a positive gives a negative.
   Expand −2(x − 1):
   (−2) × x = −2x
   (−2) × (−1) = 2
   
   The equation is now 7 − 2x + 2 = 3
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 7 + 2 make 9.
   The equation is now −2x + 9 = 3
4. Subtract 9 from both sides. This undoes the +9, because +9 − 9 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   −2x + 9 − 9 = 3 − 9
   −2x = −6
5. Divide both sides by −2. −2x means −2 multiplied by x. The inverse of multiplying by −2 is dividing by −2, and we do it to both sides to keep the balance. This leaves x on its own. Careful with signs: a positive divided by a negative gives a negative answer, and a negative divided by a negative gives a positive.
   −2x−2 = −6−2
   x = −6−2 = 3
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 7 − 2 × (3 − 1) = 7 − 2 × 2 = 7 − 4 = 3. Right side: 3. Both sides equal 3, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   20 − 3(x + 1) = 2
2. Expand the brackets. Multiply each term inside the bracket by the number outside it. A negative number multiplied by a negative number gives a positive answer, and a negative multiplied by a positive gives a negative.
   Expand −3(x + 1):
   (−3) × x = −3x
   (−3) × 1 = −3
   
   The equation is now 20 − 3x − 3 = 2
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 20 − 3 make 17.
   The equation is now −3x + 17 = 2
4. Subtract 17 from both sides. This undoes the +17, because +17 − 17 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   −3x + 17 − 17 = 2 − 17
   −3x = −15
5. Divide both sides by −3. −3x means −3 multiplied by x. The inverse of multiplying by −3 is dividing by −3, and we do it to both sides to keep the balance. This leaves x on its own. Careful with signs: a positive divided by a negative gives a negative answer, and a negative divided by a negative gives a positive.
   −3x−3 = −15−3
   x = −15−3 = 5
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 20 − 3 × (5 + 1) = 20 − 3 × 6 = 20 − 18 = 2. Right side: 2. Both sides equal 2, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   5 − (x − 3) = 1
2. Expand the brackets. Multiply each term inside the bracket by the number outside it. A negative number multiplied by a negative number gives a positive answer, and a negative multiplied by a positive gives a negative.
   Expand −(x − 3):
   (−1) × x = −x
   (−1) × (−3) = 3
   
   The equation is now 5 − x + 3 = 1
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 5 + 3 make 8.
   The equation is now −x + 8 = 1
4. Subtract 8 from both sides. This undoes the +8, because +8 − 8 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   −x + 8 − 8 = 1 − 8
   −x = −7
5. Divide both sides by −1. −x means −1 multiplied by x. The inverse of multiplying by −1 is dividing by −1, and we do it to both sides to keep the balance. This leaves x on its own. Careful with signs: a positive divided by a negative gives a negative answer, and a negative divided by a negative gives a positive.
   −x−1 = −7−1
   x = −7−1 = 7
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 7

Check. Substitute x = 7 into the original equation. Left side: 5 − (7 − 3) = 5 − 4 = 1. Right side: 1. Both sides equal 1, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   12 − 2(x + 3) = 4
2. Expand the brackets. Multiply each term inside the bracket by the number outside it. A negative number multiplied by a negative number gives a positive answer, and a negative multiplied by a positive gives a negative.
   Expand −2(x + 3):
   (−2) × x = −2x
   (−2) × 3 = −6
   
   The equation is now 12 − 2x − 6 = 4
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 12 − 6 make 6.
   The equation is now −2x + 6 = 4
4. Subtract 6 from both sides. This undoes the +6, because +6 − 6 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   −2x + 6 − 6 = 4 − 6
   −2x = −2
5. Divide both sides by −2. −2x means −2 multiplied by x. The inverse of multiplying by −2 is dividing by −2, and we do it to both sides to keep the balance. This leaves x on its own. Careful with signs: a positive divided by a negative gives a negative answer, and a negative divided by a negative gives a positive.
   −2x−2 = −2−2
   x = −2−2 = 1
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 1

Check. Substitute x = 1 into the original equation. Left side: 12 − 2 × (1 + 3) = 12 − 2 × 4 = 12 − 8 = 4. Right side: 4. Both sides equal 4, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   9 − 3(x − 2) = 6
2. Expand the brackets. Multiply each term inside the bracket by the number outside it. A negative number multiplied by a negative number gives a positive answer, and a negative multiplied by a positive gives a negative.
   Expand −3(x − 2):
   (−3) × x = −3x
   (−3) × (−2) = 6
   
   The equation is now 9 − 3x + 6 = 6
3. Collect like terms on each side. Like terms are terms with the same letter part: all the x terms go together, and all the plain numbers go together. Doing this makes each side as short as possible.
   On the left side: the numbers 9 + 6 make 15.
   The equation is now −3x + 15 = 6
4. Subtract 15 from both sides. This undoes the +15, because +15 − 15 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   −3x + 15 − 15 = 6 − 15
   −3x = −9
5. Divide both sides by −3. −3x means −3 multiplied by x. The inverse of multiplying by −3 is dividing by −3, and we do it to both sides to keep the balance. This leaves x on its own. Careful with signs: a positive divided by a negative gives a negative answer, and a negative divided by a negative gives a positive.
   −3x−3 = −9−3
   x = −9−3 = 3
6. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 9 − 3 × (3 − 2) = 9 − 3 × 1 = 9 − 3 = 6. Right side: 6. Both sides equal 6, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   2(x + 3) = 10
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 2(x + 3):
   2 × x = 2x
   2 × 3 = 6
   
   The equation is now 2x + 6 = 10
3. Subtract 6 from both sides. This undoes the +6, because +6 − 6 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   2x + 6 − 6 = 10 − 6
   2x = 4
4. Divide both sides by 2. 2x means 2 multiplied by x. The inverse of multiplying by 2 is dividing by 2, and we do it to both sides to keep the balance. This leaves x on its own.
   2x2 = 42
   x = 42 = 2
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 2

Check. Substitute x = 2 into the original equation. Left side: 2 × (2 + 3) = 2 × 5 = 10. Right side: 10. Both sides equal 10, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   3(x − 1) = 12
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 3(x − 1):
   3 × x = 3x
   3 × (−1) = −3
   
   The equation is now 3x − 3 = 12
3. Add 3 to both sides. This undoes the −3, because −3 + 3 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   3x − 3 + 3 = 12 + 3
   3x = 15
4. Divide both sides by 3. 3x means 3 multiplied by x. The inverse of multiplying by 3 is dividing by 3, and we do it to both sides to keep the balance. This leaves x on its own.
   3x3 = 153
   x = 153 = 5
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 5

Check. Substitute x = 5 into the original equation. Left side: 3 × (5 − 1) = 3 × 4 = 12. Right side: 12. Both sides equal 12, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.

Key words. An equation says that two things are equal, for example 3x + 5 = 20. To solve it means to find the value of the letter that makes it true. The inverse operation is the operation that undoes another: adding and subtracting undo each other, and multiplying and dividing undo each other. An equation is like a pair of balanced scales: whatever you do to one side you must do to the other side. A bracket such as 3(x + 2) means 3 multiplied by everything inside. Expanding the bracket means multiplying each term inside by the number outside.

Method. Solve the equation by using inverse operations (the opposite operation) on both sides, so that the equation stays balanced, until the letter x is on its own.

1. Write down the equation. The two sides of an equation are equal, like the two sides of a balanced pair of scales. We want the value of x that keeps them balanced.
   4(x + 2) = 20
2. Expand the brackets. Multiply each term inside the bracket by the number outside it.
   Expand 4(x + 2):
   4 × x = 4x
   4 × 2 = 8
   
   The equation is now 4x + 8 = 20
3. Subtract 8 from both sides. This undoes the +8, because +8 − 8 = 0, which leaves the x term on its own. We do it to both sides to keep the balance.
   4x + 8 − 8 = 20 − 8
   4x = 12
4. Divide both sides by 4. 4x means 4 multiplied by x. The inverse of multiplying by 4 is dividing by 4, and we do it to both sides to keep the balance. This leaves x on its own.
   4x4 = 124
   x = 124 = 3
5. Write the solution. x is now on its own, so the equation tells us its value.
   x = 3

Check. Substitute x = 3 into the original equation. Left side: 4 × (3 + 2) = 4 × 5 = 20. Right side: 20. Both sides equal 20, so the solution is correct. ✓

Watch out. Multiply every term inside the bracket by the number outside, not just the first one. Take care with a minus sign in front of a bracket: it changes the sign of every term inside.