Linear Equations & Inequalities
Solve linear equations with the unknown on one or both sides, and solve and represent simple linear inequalities.
Overview
An equation says two things are equal and is solved by finding the value of the unknown. In Year 8 students solve harder linear equations — including ones with brackets and with the unknown on both sides — and meet inequalities, which describe a range of values rather than a single answer. Solving equations is the single most-used skill in the whole of algebra.
What You Will Learn
- Solve linear equations using inverse operations (two or more steps)
- Solve equations that contain brackets by expanding first
- Solve equations with the unknown on both sides
- Understand and use the inequality symbols <, >, ≤ and ≥
- Solve a simple linear inequality and show the solution on a number line
Key Vocabulary
Common Mistakes to Avoid
- Doing the same operation to only one side of the equation
- Getting the inverse operation wrong, e.g. adding instead of subtracting
- Forgetting to expand the bracket before solving
- Treating an inequality exactly like an equation and losing the < or > sign in the answer
What Comes Next
In Year 9 this leads to solving equations with fractions and to simultaneous equations, and at IGCSE to rearranging formulae and solving quadratics — all part of the Algebra and Graphs topic.
Frequently Asked Questions
How do I solve an equation with x on both sides?
Collect the unknowns on one side first by adding or subtracting one of the x terms from both sides. For 5x = 2x + 9, subtract 2x from both sides to get 3x = 9, then divide by 3 to get x = 3.
What does the inequality 3 < x ≤ 7 mean?
It describes all the values of x that are greater than 3 and less than or equal to 7. The ≤ means 7 is included, but the < means 3 is not. On a number line you would use an open circle at 3 and a filled circle at 7.
Study This Topic
Topic Details
- Stage
- Year 8
- Strand
- Algebra
- Framework ref
- 8Ae
- Difficulty
- Medium
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) →