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Grade 5 · Foundation and Higher · free GCSE maths worksheet

Solving inequalities with more than one step

Including negative multipliers on Higher.

17 original questions, 57 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

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

Write down all the possible values of n.

2 marks
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-2, -1, 0, 1, 2
4

The diagram shows an inequality on a number line.

Write down the inequality shown, using x.

−3−2−10123456
2 marks
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-1 <= x < 4
5

Solve 5x − 2 > 3x + 10

3 marks
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x > 6
6

Solve 7x − 4 > 3x + 12

3 marks
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x > 4
7

Solve 2x5 − 1 < 3

3 marks
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x < 10
8

Solve 2(3x − 5) < 4(x + 1)

3 marks
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x < 7
9
  1. Solve 3(x − 1) ≥ 6
  2. Show your solution on the number line.
−2−1012345678
3 marks
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a) x >= 3 b) Solid circle at 3 with a line and arrow pointing right
10

Solve 5 − 2x ≥ 17

3 marks
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x <= -6
11

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
12

Solve 10 − 3x ≤ 2x + 25

3 marks
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x >= -3
13
  1. Solve −3 < 2x + 1 ≤ 9
  2. Write down all the integer values of x that satisfy your answer to part a.
4 marks
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a) -2 < x <= 4 b) -1, 0, 1, 2, 3, 4
14

n is an integer.

n satisfies both 2n + 5 > −1 and 4 − n ≥ 1

Write down all the possible values of n.

4 marks
Show answer
-2, -1, 0, 1, 2, 3
15
  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
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a) -3, -2, -1 b) y > 5
16
  1. Solve 5 − 2x ≥ 1
  2. Factorise x2 + 5x + 6
5 marks
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a) x <= 2 b) (x + 2)(x + 3)
17
  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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