Linear Inequalities

15 questions with answers and video solutions. Try each one before revealing the answer.

Solve:

\displaystyle 4x+2\lt9

Solve:

\displaystyle 4\gt 2z-5

Solve the inequality:

\displaystyle 10\lt 7-3x

Solve:

\displaystyle 3a-2\ge4+5a

Solve

\displaystyle \frac{2}{3}x+4\gt 10-2(x-1)

Solve the inequation

\displaystyle \large\frac{x\,+\,2}{5}\normalsize \gt -\large\frac{3x}{4}\normalsize

Solve:

\displaystyle \frac{3}{4}(x-5)-\frac{1}{6}(x+2)\gt 7

Solve:

\displaystyle \frac{r}{6} \leq \frac{1}{8}-r

2015 P1 Q2

3 Marks

Solve algebraically the inequality
$\displaystyle 11-2(1+3x)\lt 39$

2017 P1 Q8

3 Marks

Solve, algebraically, the inequality $\displaystyle 19+x>15+3(x-2).$

2018 P2 Q4

3 Marks

Solve, algebraically, the inequation $\displaystyle 3x<6(x-1)-12.$

2021 P1 Q11

Solve, algebraically, the inequation
$\displaystyle 1-(x+4)\gt 2x$

2023 P1 Q14

3 Marks

Solve, algebraically, the inequation
$\displaystyle \large\frac{x\ +\ 1}{3}\normalsize -2\gt\large\frac{3x}{5}\normalsize$

2024 P2 Q4

3 Marks

Solve, algebraically, the inequation
$\displaystyle 5(x-2)+4 < 7x+8.$

2026 P1 Q4

3 Marks

Solve, algebraically, the inequation

\displaystyle x+8 \lt 3(x-2)+20.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.