Success TutoringWorksheets

8th Grade Linear Equations Topic Test — Answers

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

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheet8th Grade · Mathematics · Linear Equations

8th Grade Linear Equations Topic Test — Answers

Part A: Expanding Expressions (Distributive Property)

1.Expand: 5(4x − 4)[1 mark]

Answer: 20x − 20

  1. 5 × 4x = 20x
  2. 5 × −4 = −20
2.Expand: 4(4x + 7)[1 mark]

Answer: 16x + 28

  1. 4 × 4x = 16x
  2. 4 × 7 = 28
3.Expand: 5(6x − 8)[1 mark]

Answer: 30x − 40

  1. 5 × 6x = 30x
  2. 5 × −8 = −40
4.Expand: 6(6x − 5)[1 mark]

Answer: 36x − 30

  1. 6 × 6x = 36x
  2. 6 × −5 = −30
5.Expand: 6(5x + 4)[1 mark]

Answer: 30x + 24

  1. 6 × 5x = 30x
  2. 6 × 4 = 24
6.Expand: −4(5x + 5)[1 mark]

Answer: −20x − 20

  1. −4 × 5x = −20x
  2. −4 × 5 = −20

Part B: Solving Linear Equations

7.3x − 13 = −16[2 marks]

Answer: x = −1

  1. Add 13 to both sides: 3x = −3
  2. Divide both sides by 3: x = −1
8.2x + 4 = 14[2 marks]

Answer: x = 5

  1. Subtract 4 from both sides: 2x = 10
  2. Divide both sides by 2: x = 5
9.6x + 5 = 41[2 marks]

Answer: x = 6

  1. Subtract 5 from both sides: 6x = 36
  2. Divide both sides by 6: x = 6
10.6x − 9 = −15[2 marks]

Answer: x = −1

  1. Add 9 to both sides: 6x = −6
  2. Divide both sides by 6: x = −1
11.3x − 1 = −10[2 marks]

Answer: x = −3

  1. Add 1 to both sides: 3x = −9
  2. Divide both sides by 3: x = −3
12.8x − 1 = 47[2 marks]

Answer: x = 6

  1. Add 1 to both sides: 8x = 48
  2. Divide both sides by 8: x = 6
13.8x − 4 = 36[2 marks]

Answer: x = 5

  1. Add 4 to both sides: 8x = 40
  2. Divide both sides by 8: x = 5
14.6x − 13 = −67[2 marks]

Answer: x = −9

  1. Add 13 to both sides: 6x = −54
  2. Divide both sides by 6: x = −9

Part C: Solving Linear Equations

15.5(x + 8) = 0[2 marks]

Answer: x = −8

  1. Expand: 5x + 40 = 0
  2. Subtract 40: 5x = −40
  3. Divide by 5: x = −8
16.4x + 5 = 2x + 13[2 marks]

Answer: x = 4

  1. Subtract 2x from both sides: 2x + 5 = 13
  2. Subtract 5: 2x = 8
  3. Divide by 2: x = 4
17.3x − 10 = x + 8[2 marks]

Answer: x = 9

  1. Subtract 1x from both sides: 2x − 10 = 8
  2. Add 10: 2x = 18
  3. Divide by 2: x = 9
18.4(x + 2) = 52[2 marks]

Answer: x = 11

  1. Expand: 4x + 8 = 52
  2. Subtract 8: 4x = 44
  3. Divide by 4: x = 11
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: