Fiducia TogetherInequalities
Statements about ranges of values rather than a single answer.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
An inequality uses <, >, ≤ or ≥ instead of an equals sign, and its solution is a range of values.
Where it applies
Both tiers. Quadratic inequalities and regions on graphs are higher tier.
How it works
Inequalities are solved like equations with one exception: multiplying or dividing by a negative number reverses the sign.
On a number line, an open circle excludes the value and a filled circle includes it. On a graph, a dashed line excludes and a solid line includes.
How to use it in your work
Watch the sign reversal when dividing by a negative. It is the classic error.
Draw the number line or shade the region — questions often ask for the representation as well as the algebra.
For integer solutions, list them; do not leave the answer as a range if the question wants values.
Where to get help
Your teacher and your board's specification. Bitesize for worked examples, and the subject song for the topic list.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.