Inequalities

Find the integers $n$ which make $20<4n-3<30$ true.

May/June 2015

Solve the inequality $-4 \leq 2x - 5 < 7$.

May/June 2015

The shaded part of the diagram is described by three inequalities. One of them is $y > \frac{1}{2}x + 2$.

May/June 2016

The diagram displays the lines $x + y = 8$ and $2y = x + 4$.

May/June 2016

Find which integers satisfy $1 < 3x + 5 \leq 11$.

May/June 2018

Solve the compound inequality $10 < 3(x + 1) \le 24$ for $x$.

May/June 2019

Represent the inequality $-3 < x \leq 2$ on the number line shown below.

May/June 2019

Solve the inequality given by $x - 5 > 3x + 7$.

May/June 2023

A $1\text{ cm}$ square grid shows three lines together with a shaded region.

May/June 2023

Write down every integer value of $x$ that makes the inequality $-3 \leq x < 1$ true.

May/June 2025

The numbers in the list are $-8, -5, -3, -2, 0, 2, 4, 9$.

Oct/Nov 2015

Write $6x^2y^3 - 15x^3y$ in fully factorised form.

Oct/Nov 2015

Solve $12-2x<x$.

Oct/Nov 2017

Find the two negative integers that solve $\frac{x}{3} - 1 < \frac{3x}{4}$.

Oct/Nov 2017

Find the values that $x$ can take, given that $x$ is an integer and $15 < 2x - 3 < 22$.

Oct/Nov 2018

The diagram displays the lines $x + y = 8$, $y = \frac{1}{2}x$, $x = 0$ and $y = 0$. The spaces enclosed by the lines are marked using letters.

Oct/Nov 2019

Find the solution to the inequality $23 + 2n > 5 - 6n$.

Oct/Nov 2021

Plot the inequality $-4 \le x < 2$ on the number line.

Oct/Nov 2022

Solve the inequality $7m - 13 \leq 8$.

Oct/Nov 2023

The diagram depicts the lines $y = 2x + 1$ and $x + y = 2$.

Oct/Nov 2024

State the inequality shown on the number line.

Oct/Nov 2025