Equations give you ONE answer: x = 5. But life often needs ranges! "You must be at least 16 to drive" means age ≥ 16. "The bag must weigh less than 23kg" means weight < 23. Inequalities describe these ranges - and we can solve them just like equations (with one important twist!).

Visual: Number Line Representations

Diagram showing inequalities on number lines: open circles for < and > (not including the value), closed circles for ≤ and ≥ (including the value). Shows examples of x > 3, x ≤ 2, and compound inequality -1 < x ≤ 3. Warning box about flipping the sign when multiplying/dividing by negative.

This introduction covers Not Just Equals! within Linear Inequalities for GCSE Mathematics. Revise Linear Inequalities in Algebra for GCSE Mathematics with 14 exam-style questions and 11 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 1 of 8 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Practice questions for Linear Inequalities

Which of the following correctly describes how to represent x > 3 on a number line?

A. A closed (filled) circle at 3, with an arrow pointing to the right
B. An open (empty) circle at 3, with an arrow pointing to the right
C. An open (empty) circle at 3, with an arrow pointing to the left
D. A closed (filled) circle at 3, with an arrow pointing to the left

1 markfoundation

When solving an inequality, the direction of the inequality sign must reverse if you multiply or divide both sides by a negative number. Explain why this rule is necessary. You may use an example to support your explanation.

2 marksstandard

Quick recall flashcards

The Flip Rule for inequalities

When you multiply or divide BOTH sides by a NEGATIVE number, you MUST reverse (flip) the inequality sign. Example: -2x > 6 becomes x < -3

Open vs Closed Circle on a number line

Open circle (hollow) for < and > — endpoint NOT included. Closed circle (filled) for ≤ and ≥ — endpoint IS included.

Not Just Equals!

Visual: Number Line Representations

Practice questions for Linear Inequalities

Quick recall flashcards

14 questions on Linear Inequalities: practise free