Solving and and Graphing Inequalities for GCSE Maths (with Examples and Questions)

Inequalities are a key topic in GCSE maths, helping you understand how to express and solve conditions that involve ranges of values rather than exact numbers.

At GCSE level, you'll learn how to solve inequalities using algebraic methods and represent solutions on number lines and graphs. Mastering inequalities is essential for tackling exam questions and applying mathematical reasoning in real-world contexts.

This page covers solving and graphing linear inequalities, with clear explanations and practice questions to support your learning.

Solving Inequalities

Learn how to solve linear inequalities step by step, including dealing with inequalities involving brackets and fractions.

Watch this video to learn how to solve inequalities with only one inequality sign.

For example 3x + 1 < 5 includes only one inequality sign.

Inequalities can also include two (or more) inequality signs.

You could, for example, be asked to solve 2 < 4x - 6 < 12.

Watch this video to learn how to solve inequalities with two signs.

Graphing Inequalities and Shading Regions

This video helps you to understand how to graph inequalities with 2 variables on coordinate grids (in 2D), with guidance on how to shade inequality regions correctly.

The rest of the lesson on inequalities is not quite ready, but if you already know what you're doing, we have practice questions linked below.