Algebra · Guided Practice

Linear Inequalities

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

1
Solve: 4x+2<9\displaystyle 4x+2\lt9

No hints on this one — its full written solution is with the answer.

2
Solve: 4>2z−5\displaystyle 4\gt 2z-5

No hints on this one — its full written solution is with the answer.

3
Solve the inequality: 10<7−3x\displaystyle 10\lt 7-3x

No hints on this one — its full written solution is with the answer.

4
Solve: 3a−2≥4+5a\displaystyle 3a-2\ge4+5a

No hints on this one — its full written solution is with the answer.

5
Solve
23x+4>10−2(x−1)\displaystyle \frac{2}{3}x+4\gt 10-2(x-1)

No hints on this one — its full written solution is with the answer.

6
Solve the inequation
x + 25>−3x4\displaystyle \large\frac{x\,+\,2}{5}\normalsize \gt -\large\frac{3x}{4}\normalsize

No hints on this one — its full written solution is with the answer.

7
Solve: 34(x−5)−16(x+2)>7\displaystyle \frac{3}{4}(x-5)-\frac{1}{6}(x+2)\gt 7

No hints on this one — its full written solution is with the answer.

8
Solve: r6≤18−r\displaystyle \frac{r}{6} \leq \frac{1}{8}-r

No hints on this one — its full written solution is with the answer.

9
2015 P1 Q2
3 Marks

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

10
2017 P1 Q8
3 Marks

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

11
2018 P2 Q4
3 Marks

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

12
2021 P1 Q11

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

No hints on this one — its full written solution is with the answer.

13
2023 P1 Q14
3 Marks

Solve, algebraically, the inequation
x + 13−2>3x5\displaystyle \large\frac{x\ +\ 1}{3}\normalsize -2\gt\large\frac{3x}{5}\normalsize

14
2024 P2 Q4
3 Marks

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

15
2026 P1 Q4
3 Marks
Solve, algebraically, the inequation
x+8<3(x−2)+20.\displaystyle x+8 \lt 3(x-2)+20.

Keep practising

More linear inequalities questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

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

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