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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Solving linear inequalities on a number line

Solving and showing the solution set.

19 original questions, 60 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

n is an integer.

−2 < n ≤ 3

Write down all the possible values of n.

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

Solve 4x + 3 < 19

2 marks
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x < 4
3

Write down the inequality shown by each number line.

  1. A closed circle at 3 with the arrow pointing left.
  2. An open circle at −2 with the arrow pointing right.
2 marks
Show answer
a) x ≤ 3 b) x > -2
4

Describe how to show each inequality on a number line. Say what kind of circle to use at each end and which way the arrow points.

  1. x ≥ 4
  2. x < −1
2 marks
Show answer
a) closed circle at 4, arrow pointing right b) open circle at -1, arrow pointing left
5

n is an integer such that n > −3 and 2n + 1 ≤ 5

Write down all the possible values of n.

2 marks
Show answer
-2, -1, 0, 1, 2
6

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
7

x is an integer.
−3 < x ≤ 2

Write down all the possible values of x.

2 marks
Show answer
-2, -1, 0, 1, 2
8

Solve 5x − 2 > 3x + 10

3 marks
Show answer
x > 6
9

Solve 2x5 − 1 < 3

3 marks
Show answer
x < 10
10
  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
11

Solve 3x − 5 ≥ 10

Describe how to show your answer on a number line.

3 marks
Show answer
x ≥ 5; closed circle at 5, arrow pointing right
12

A number line has an open circle at −1 with the arrow pointing left, and a closed circle at 3 with the arrow pointing right.

  1. Write down the inequalities shown by the number line.
  2. Is x = 3 a solution? Is x = −1 a solution?
3 marks
Show answer
a) x < -1 or x ≥ 3 b) x = 3 yes; x = -1 no
13

Chloe wants to show x > 2 on a number line.

She draws a solid circle at 2 with an arrow pointing to the right.

  1. Explain the mistake Chloe has made.
  2. Write down the greatest integer that satisfies 4x − 3 < 18
4 marks
Show answer
a) The circle at 2 should be open, not solid, because x > 2 does not include 2 b) 5
14
  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
15

Solve 7 − 2x > 1

Write down the positive integers that satisfy the inequality.

3 marks
Show answer
a) x < 3 b) 1, 2
16

x is an integer. x satisfies both 2x − 1 > 5 and x + 4 ≤ 11.

Solve each inequality and write down all the possible values of x. Describe the number line for the values that satisfy both inequalities.

4 marks
Show answer
x > 3 and x ≤ 7; x = 4, 5, 6, 7
17
  1. n is an integer with −4 < n ≤ −1
    Write down all the possible values of n.
  2. Solve 7y − 3 > 2y + 22 and show your solution on the number line.
012345678910
5 marks
Show answer
a) -3, -2, -1 b) y > 5
18
  1. Solve 5 − 2x ≥ 1
  2. Factorise x2 + 5x + 6
5 marks
Show answer
a) x <= 2 b) (x + 2)(x + 3)
19
  1. n is an integer with −5 ≤ n < −1
    Write down all the possible values of n.
  2. Solve 4(x + 3) > 2x + 17
  3. Write down the smallest integer that satisfies your answer to part b.
6 marks
Show answer
a) -5, -4, -3, -2 b) x > 2.5 c) 3

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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