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Year 8 Linear Equations Topic Test — Answers

Answer sheet with worked solutions for the Year 8 linear equations topic test.

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Year 8 · Mathematics · Linear Equations

Year 8 Linear Equations Topic Test — Answers

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Part A — Expanding Brackets

1.Expand: −4(x − 2)[1 mark]

Answer: −4x + 8

  1. −4 × x = −4x
  2. −4 × −2 = 8
2.Expand: 5(2x − 6)[1 mark]

Answer: 10x − 30

  1. 5 × 2x = 10x
  2. 5 × −6 = −30
3.Expand: −1(3x − 8)[1 mark]

Answer: −3x + 8

  1. −1 × 3x = −3x
  2. −1 × −8 = 8
4.Expand: −4(4x − 9)[1 mark]

Answer: −16x + 36

  1. −4 × 4x = −16x
  2. −4 × −9 = 36
5.Expand: 4(5x − 9)[1 mark]

Answer: 20x − 36

  1. 4 × 5x = 20x
  2. 4 × −9 = −36
6.Expand: 4(x + 9)[1 mark]

Answer: 4x + 36

  1. 4 × x = 4x
  2. 4 × 9 = 36

Part B — Solving Linear Equations

7.4x + 11 = 15[2 marks]

Answer: x = 1

  1. Subtract 11 from both sides: 4x = 4
  2. Divide both sides by 4: x = 1
8.4x − 2 = −10[2 marks]

Answer: x = −2

  1. Add 2 to both sides: 4x = −8
  2. Divide both sides by 4: x = −2
9.2x − 1 = 21[2 marks]

Answer: x = 11

  1. Add 1 to both sides: 2x = 22
  2. Divide both sides by 2: x = 11
10.8x − 7 = −31[2 marks]

Answer: x = −3

  1. Add 7 to both sides: 8x = −24
  2. Divide both sides by 8: x = −3
11.5x − 12 = 18[2 marks]

Answer: x = 6

  1. Add 12 to both sides: 5x = 30
  2. Divide both sides by 5: x = 6
12.6x + 9 = −3[2 marks]

Answer: x = −2

  1. Subtract 9 from both sides: 6x = −12
  2. Divide both sides by 6: x = −2
13.7x + 1 = −62[2 marks]

Answer: x = −9

  1. Subtract 1 from both sides: 7x = −63
  2. Divide both sides by 7: x = −9
14.8x + 15 = −25[2 marks]

Answer: x = −5

  1. Subtract 15 from both sides: 8x = −40
  2. Divide both sides by 8: x = −5

Part C — Solving Linear Equations

15.4(x − 4) = −44[2 marks]

Answer: x = −7

  1. Expand: 4x − 16 = −44
  2. Add 16: 4x = −28
  3. Divide by 4: x = −7
16.5x + 3 = 2x + 39[2 marks]

Answer: x = 12

  1. Subtract 2x from both sides: 3x + 3 = 39
  2. Subtract 3: 3x = 36
  3. Divide by 3: x = 12
17.3(x + 4) = 3[2 marks]

Answer: x = −3

  1. Expand: 3x + 12 = 3
  2. Subtract 12: 3x = −9
  3. Divide by 3: x = −3
18.3x − 3 = 2x + 6[2 marks]

Answer: x = 9

  1. Subtract 2x from both sides: x − 3 = 6
  2. Add 3: 1x = 9
  3. Divide by 1: x = 9
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