GCSE Maths · Linear Equations · Higher · Summary

GCSE Maths Linear Equations (Higher): summary and key words

Chapter summary

Skill	Method
Equation vs expression	An equation has an = sign and can be solved; an expression cannot
One-step equations	Do the opposite operation to both sides: + and − undo each other, × and ÷ undo each other
Two-step equations	Undo + or − first, then × or ÷. Always do the same to both sides
Negative and fractional answers	Keep the sign when dividing. Leave exact fractions (or write mixed numbers); do not round unless asked
Unknown on both sides	Subtract the smaller x term from both sides, then move the plain numbers, then divide
Brackets	Expand first (multiply every term inside); a minus before a bracket changes every sign inside
Equations with fractions	Multiply every term by the LCM of the denominators; use a bracket when the top has two terms
Equations from words	Let x = … (with units); write the equation; solve; answer the question in words; check
Geometry equations	Use perimeter, angle sum 180° (triangle, straight line), 360° (point, quadrilateral), or equal sides/angles
Graphs	Solution is the x-value where the graph meets the line, or where two lines cross
Checking	Substitute into the original equation: both sides must be equal
Higher: special cases	x in the denominator: multiply by the bottom (reject a value that makes it 0). A false statement (6 = 5) means no solution; a true one (6 = 6) means every x works

I can tell an equation from an expression, and explain the balance idea.
I can solve one-step and two-step equations by doing the same to both sides.
I can solve equations with negative or fractional solutions and give the answer in a sensible form.
I can solve equations with the unknown on both sides.
I can expand brackets and solve equations that contain them.
I can solve equations that contain fractions (Higher: algebraic fractions and unknowns in denominators).
I can turn a worded problem into an equation, solve it, and answer in context.
I can use perimeter and angle facts to form and solve equations.
I can use a graph to solve an equation approximately, and decide whether a solution makes sense.
I can check a solution by substitution.

Equation: A statement that two expressions are equal, such as 3x + 5 = 20. It contains an equals sign.
Expression: A collection of numbers and letters with no equals sign, such as 3x + 5.
Unknown: A letter standing for a number we want to find.
Solve: Find the value of the unknown that makes the equation true.
Solution: The value of the unknown that makes an equation true.
Inverse operation: The operation that undoes another: + and − are inverses; × and ÷ are inverses.
Substitute: Replace a letter by a number.
Like terms: Terms with the same letter part, such as 3x and 5x.
Expand: Remove a bracket by multiplying every term inside by the number outside.
Common denominator: A bottom number that several fractions can all be changed to.
Perimeter: The total distance around the edge of a shape.
Identity (Higher): An equation that is true for every value of the unknown, such as 3(x + 2) = 3x + 6.