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Year 9 Linear Equations Topic Test — Answers

Answer sheet with worked solutions for the Year 9 linear equations topic test.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Linear Equations

Year 9 Linear Equations Topic Test — Answers

Part A: Expanding Brackets

1.Expand: 2(2x − 6)[1 mark]

Answer: 4x − 12

  1. 2 × 2x = 4x
  2. 2 × −6 = −12
2.Expand: −4(x − 7)[1 mark]

Answer: −4x + 28

  1. −4 × x = −4x
  2. −4 × −7 = 28
3.Expand: 7(x + 1)[1 mark]

Answer: 7x + 7

  1. 7 × x = 7x
  2. 7 × 1 = 7
4.Expand: −2(3x − 3)[1 mark]

Answer: −6x + 6

  1. −2 × 3x = −6x
  2. −2 × −3 = 6
5.Expand: 1(4x − 5)[1 mark]

Answer: 4x − 5

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

Answer: 10x − 5

  1. 5 × 2x = 10x
  2. 5 × −1 = −5

Part B: Solving Linear Equations

7.8x − 1 = −9[2 marks]

Answer: x = −1

  1. Add 1 to both sides: 8x = −8
  2. Divide both sides by 8: x = −1
8.9x + 6 = −3[2 marks]

Answer: x = −1

  1. Subtract 6 from both sides: 9x = −9
  2. Divide both sides by 9: x = −1
9.5x − 12 = −2[2 marks]

Answer: x = 2

  1. Add 12 to both sides: 5x = 10
  2. Divide both sides by 5: x = 2
10.3x + 7 = −20[2 marks]

Answer: x = −9

  1. Subtract 7 from both sides: 3x = −27
  2. Divide both sides by 3: x = −9
11.4x − 9 = 31[2 marks]

Answer: x = 10

  1. Add 9 to both sides: 4x = 40
  2. Divide both sides by 4: x = 10
12.7x + 5 = 68[2 marks]

Answer: x = 9

  1. Subtract 5 from both sides: 7x = 63
  2. Divide both sides by 7: x = 9
13.6x + 11 = −7[2 marks]

Answer: x = −3

  1. Subtract 11 from both sides: 6x = −18
  2. Divide both sides by 6: x = −3
14.8x + 13 = −19[2 marks]

Answer: x = −4

  1. Subtract 13 from both sides: 8x = −32
  2. Divide both sides by 8: x = −4

Part C: Solving Linear Equations

15.4(x − 2) = −28[2 marks]

Answer: x = −5

  1. Expand: 4x − 8 = −28
  2. Add 8: 4x = −20
  3. Divide by 4: x = −5
16.6x + 8 = x + 68[2 marks]

Answer: x = 12

  1. Subtract 1x from both sides: 5x + 8 = 68
  2. Subtract 8: 5x = 60
  3. Divide by 5: x = 12
17.6x − 3 = 3x − 27[2 marks]

Answer: x = −8

  1. Subtract 3x from both sides: 3x − 3 = −27
  2. Add 3: 3x = −24
  3. Divide by 3: x = −8
18.5(x − 6) = −50[2 marks]

Answer: x = −4

  1. Expand: 5x − 30 = −50
  2. Add 30: 5x = −20
  3. Divide by 5: x = −4
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