Linear Equations & Inequalities — Year 8 Revision Notes
These notes cover solving multi-step linear equations, equations with brackets and the unknown on both sides, and solving simple inequalities — all at Year 8 (Stage 8) level.
Solving multi-step equations
Solve an equation by doing the same inverse operation to both sides until the unknown is alone. To solve 3x + 5 = 20, subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5. Always undo addition and subtraction before multiplication and division.
Key Facts & Formulas
- 3x + 5 = 20 → 3x = 15 → x = 5
Tips
- Whatever you do to one side, do to the other.
- Undo + and − first, then × and ÷.
Brackets and unknowns on both sides
If an equation has a bracket, expand it first. If the unknown appears on both sides, collect the unknowns on one side and the numbers on the other. For 2(x + 3) = x + 10, expand to 2x + 6 = x + 10, subtract x from both sides to get x + 6 = 10, then x = 4.
Key Facts & Formulas
- 2(x + 3) = x + 10 → x = 4
Tips
- Expand brackets before doing anything else.
- Move the smaller x term to avoid a negative.
Solving inequalities
An inequality is solved just like an equation, using inverse operations, but the answer is a range of values rather than a single number. For 2x + 1 > 9, subtract 1 to get 2x > 8, then divide by 2 to get x > 4. Show x > 4 on a number line with an open circle at 4 and an arrow pointing right.
Key Facts & Formulas
- 2x + 1 > 9 → x > 4
Tips
- Keep the inequality sign in every line of working.
- Open circle for < or >, filled circle for ≤ or ≥.
Revision Checklist
- I can solve linear equations using inverse operations
- I can solve equations with brackets and with the unknown on both sides
- I can solve a simple linear inequality
- I can show the solution of an inequality on a number line
Frequently Asked Questions
Is the answer to an inequality a single number?
Usually not. An inequality such as x > 4 describes every value greater than 4, not just one number. That is why we show the answer on a number line or as a solution set.
Build strong foundations in Linear Equations & Inequalities
A free trial class with Teacher Rig helps your Year 8 child master Linear Equations & Inequalities now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Linear Equations & Inequalities develops in IGCSE Algebra and Graphs (Cambridge 0580) →