Robinson Tuition
Year 8 · Key Stage 3 · free KS3 maths worksheet

Linear inequalities

12 original questions, 33 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1
  1. Write "x is greater than 3" as an inequality.
  2. Write "y is at most 7" as an inequality.
  3. Is 5 a solution of x ≥ 5? Give a reason.
3 marks
Show answer
a) x > 3 b) y ≤ 7 c) Yes, because x ≥ 5 includes 5
2

n is an integer.

−2 < n ≤ 3

Write down all the possible values of n.

2 marks
Show answer
-1, 0, 1, 2, 3
3

Solve 4x + 3 < 19

2 marks
Show answer
x < 4
4

The diagram shows an inequality on a number line.

Write down the inequality shown, using x.

−3−2−10123456
2 marks
Show answer
-1 <= x < 4
5

Show each inequality on its number line.

  1. x ≥ −2
  2. −1 < x ≤ 4
−5−4−3−2−1012345a−5−4−3−2−1012345b
2 marks
Show answer
a) solid circle at -2, arrow to the right b) open circle at -1, solid circle at 4, line joining them
6

Solve 5x − 2 > 3x + 10

3 marks
Show answer
x > 6
7
  1. Solve 3(x − 1) ≥ 6
  2. Show your solution on the number line.
−2−1012345678
3 marks
Show answer
a) x >= 3 b) Solid circle at 3 with a line and arrow pointing right
8

Solve 2x5 − 1 < 3

3 marks
Show answer
x < 10
9
  1. Solve 2(3x − 1) ≤ 4x + 9
  2. Write down the largest integer that satisfies your answer to part a.
3 marks
Show answer
a) x ≤ 5.5 b) 5
10
  1. Solve 7 − 3x > 19
  2. Show your answer on the number line.
−8−7−6−5−4−3−2−1012
3 marks
Show answer
a) x < -4 b) open circle at -4, arrow to the left
11
  1. Solve −3 < 2x + 1 ≤ 9
  2. Write down all the integer values of x that satisfy your answer to part a.
4 marks
Show answer
a) -2 < x <= 4 b) -1, 0, 1, 2, 3, 4
12

Solve x + 53 ≥ x − 1

3 marks
Show answer
x ≤ 4

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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