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 $-4 \le 2x + 2 < 10$ (3 marks)

(b) Write down all the integer values of $x$ that satisfy the inequality in part (a). (1 mark)
Level 3 · 4 marksTry it
2
$-4 < n \le 3$

$n$ is an integer.
(a) Write down the least possible value of $n$ .

(1 mark)
(b) On the number line below, show the inequality $-2 \le y < 4$ (2 marks)
(c) Solve $\dfrac{3}{4}w + 5 < 17$

(3 marks)
Level 3 · 6 marksTry it
3
Solve the inequality $4x - 3 < 17$
Level 3 · 2 marksTry it
4
$n$ is an integer and $-2 < n \le 3$

Write down all the possible values of $n$ .
Level 3 · 2 marksTry it
5
$n$ is an integer.

$n$ satisfies both of the inequalities

$-4 < n \le 1 \qquad \text{and} \qquad n > -2$

Write down all the possible values of $n$ .
Level 3 · 2 marksTry it