What is important to know about Inequalities?

means "greater than", ≤ means "less than or equal to", ≥ means "greater than or equal to".

What is important to know about Inequalities?

Solve inequalities like equations — but if you multiply or divide by a negative number, flip the inequality sign.

What is important to know about Inequalities?

The solution to a linear inequality is a range of values.

What are common mistakes with Inequalities?

Including the endpoint for a strict inequality ( ) when listing integers.

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Algebra · Foundation & Higher

Inequalities

Q: What are common mistakes with Inequalities?

Not flipping the sign when multiplying or dividing by a negative number.

Inequalities show that one expression is greater than, less than, or equal to another. They are solved like equations, with one important exception.

Revising inequalities the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Inequalities GCSE” on the site for the complete guide.

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Key facts to remember

1< means "less than", > means "greater than", ≤ means "less than or equal to", ≥ means "greater than or equal to".
2Solve inequalities like equations — but if you multiply or divide by a negative number, flip the inequality sign.
3The solution to a linear inequality is a range of values.
4On a number line: open circle ○ for strict inequalities (< or >); closed circle ● for ≤ or ≥.

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Worked examples

Example 1

Solve 3x − 4 > 11 and represent on a number line.

Working

Add 4 to both sides: 3x > 15
Divide by 3: x > 5
Number line: open circle at 5, arrow pointing right

Answerx > 5

Example 2

List the integers that satisfy −2 ≤ x < 4

Working

x can be −2, −1, 0, 1, 2, 3 (not 4, since x < 4)

Answer−2, −1, 0, 1, 2, 3

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Common mistakes

✗Not flipping the sign when multiplying or dividing by a negative number.

✗Including the endpoint for a strict inequality (< or >) when listing integers.

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Exam tips

✓If a question says "integer values", list them — don't just write the inequality.

✓Check by substituting a value from your solution range back in.

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