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Linear Inequalities

Revise Linear Inequalities in Algebra for GCSE Mathematics with 14 exam-style questions and 11 flashcards. This is a high-frequency exam topic, so students should expect to explain it clearly under timed conditions.

Study this topic

1

Not Just Equals!

Introduction2

The Four Inequality Symbols

Key Facts3

Solving Inequalities (Like Equations!)

Deep Dive4

Worked Example 1: Simple Inequality

Notes5

Worked Example 2: Negative Coefficient (FLIP!)

Notes6

Worked Example 3: Compound Inequality

Notes7

Common Mistakes to Avoid

Exam Tips

Sample 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.

Sample Questions

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

14

exam-style questions

11

revision flashcards

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