GCSE & IGCSE maths practice

Inequalities questions and answers

Solve an inequality like an equation, keeping the inequality sign: $3x + 2 > 14$ gives $x > 4$ . The one difference: if you multiply or divide by a negative number, flip the sign. On a number line, an open circle means the end isn't included ( $<$ , $>$ ) and a filled circle means it is ( $\le$ , $\ge$ ).

8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Linear inequalities: lesson Inequality calculator

Where inequalities comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: solve linear inequalities in one variable and show them on a number line. Higher only: quadratic inequalities, set notation and inequalities on a graph.
Cambridge IGCSE (0580)	Core: represent and interpret inequalities, including on a number line. Extended: construct, solve and interpret linear inequalities, including in two variables graphically.

The method

Do the same to both sides, as with an equation.
Multiplying or dividing by a negative: reverse the sign.
Double inequalities: do the same to all three parts.
Integer values: list the whole numbers that fit, checking the ends.

Inequalities questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Solve $3x + 2 > 14$

x >

Question 2Warm-upFoundation

Solve $5x - 3 \le 22$

x ≤

Exam-style

Question 3Exam-styleFoundation

Solve $2(x + 3) < 20$

x <

Question 4Exam-styleFoundation

List the integers $n$ such that $-2 < n \le 3$ .

Question 5Exam-styleFoundation

Solve $7 - 2x \ge 1$

x ≤

Question 6Exam-styleFoundation

List the integer values of $x$ such that $-3 \le 2x + 1 < 9$ .

Challenge

Question 7ChallengeFoundation

A number line shows an open circle at 2 with an arrow pointing right. Which inequality does it show?

Question 8ChallengeHigher

Solve $x^2 < 9$

Common mistakes

Forgetting to flip the sign when dividing by a negative.
Including an end point that isn't included (< not ≤).
Writing an equals sign in the answer.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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