GCSE MATHS PRACTICE

GCSE Inequalities Questions

An inequality describes a range of values: < means less than, > greater than, and ≤ or ≥ includes equality. Solve using the same operation on both sides, but reverse the sign when multiplying or dividing by a negative number. On a number line, an open circle excludes the endpoint and a filled circle includes it; the arrow shows the allowed direction.

Updated 11 October 2026

Worked example

Solve 3x + 2 ≤ 14 and represent the solution on a number line.

Subtract 2 from both sides: 3x ≤ 12.
Divide both sides by positive 3: x ≤ 4. The sign stays the same.
The filled circle at 4 includes 4. The arrow to the left includes every smaller value.

Answer: x ≤ 4

Practice questions

1
Solve x + 5 > 9.
2
Write the inequality represented on this number line.
Enlarged diagram
100%Scroll to inspect when enlarged.
3
Solve 5x − 7 ≤ 18.
4
Solve 8 − 3x ≥ 20.

Show answers

1. x > 4
2. x > −2
3. x ≤ 5
4. x ≤ −4

Common mistakes

Keeping the sign after dividing by a negative — Multiplication or division by a negative reverses the inequality sign.
Using the wrong endpoint — Open circles mean < or >; filled circles mean ≤ or ≥.
Treating an inequality as one answer — The solution usually describes a range of values, not just its boundary.

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GCSE MATHS PRACTICE

GCSE Inequalities Questions

Updated 11 October 2026

Worked example

Solve 3x + 2 ≤ 14 and represent the solution on a number line.

Subtract 2 from both sides: 3x ≤ 12.
Divide both sides by positive 3: x ≤ 4. The sign stays the same.
The filled circle at 4 includes 4. The arrow to the left includes every smaller value.

Answer: x ≤ 4

Practice questions

1
Solve x + 5 > 9.
2
Write the inequality represented on this number line.
Enlarged diagram
100%Scroll to inspect when enlarged.
3
Solve 5x − 7 ≤ 18.
4
Solve 8 − 3x ≥ 20.

Show answers

1. x > 4
2. x > −2
3. x ≤ 5
4. x ≤ −4

Common mistakes

Keeping the sign after dividing by a negative — Multiplication or division by a negative reverses the inequality sign.
Using the wrong endpoint — Open circles mean < or >; filled circles mean ≤ or ≥.
Treating an inequality as one answer — The solution usually describes a range of values, not just its boundary.

GCSE Inequalities Questions

Worked example

Practice questions

Common mistakes

Related resources

GCSE Inequalities Questions

Worked example

Practice questions

Common mistakes

Related resources