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Not Just Equals!

Part of Linear Inequalities — GCSE Mathematics

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 7 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 7

Practice

14 questions

Recall

11 flashcards

Not Just Equals!

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.

Keep building this topic

Read this section alongside the surrounding pages in Linear Inequalities. That gives you the full topic sequence instead of a single isolated revision point.

The Four Inequality SymbolsSolving Inequalities (Like Equations!)Worked Example 1: Simple Inequality

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.

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The Four Inequality Symbols