GCSE · Inequalities

Linear inequalitiesExam-style questions

Why inequalities solve like equations except for one rule — flipping on a negative multiplier — why the answer is a RANGE not a number, and how double inequalities and integer lists work.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
(a) Solve the inequality $7 - 2x > 1$

(b) Write down the largest integer that satisfies $7 - 2x > 1$
Level 4 · 3 marksTry it
2
(a) Solve the inequality $3 < 2x + 1 \le 9$

(b) $x$ is an integer. Write down all the values of $x$ that satisfy $3 < 2x + 1 \le 9$
Level 4 · 3 marksTry it
3
A van-hire company charges a fixed fee of £40 plus £22 per day.

Amy can spend at most £150.

Work out the greatest number of whole days Amy can hire the van for.
Level 4 · 3 marksTry it
4
Solve the inequality $5 - 3x \le -7$
Level 4 · 2 marksTry it
5
(a) Solve the inequality $-5 \le 3x + 1 < 10$

(b) $x$ is an integer. Write down all the values of $x$ that satisfy $-5 \le 3x + 1 < 10$
Level 4 · 3 marksTry it