Year 8 Solving Linear Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 8 linear equations worksheet.
Year 8 · Mathematics · Linear Equations
Year 8 Solving Linear Equations Worksheet — Level 3 — Answers
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Solve each equation. Show every step and check your answer by substituting it back in.
1.8x − 2 = 3x + 33
Answer: x = 7
- Subtract 3x from both sides: 5x − 2 = 33
- Add 2: 5x = 35
- Divide by 5: x = 7
2.9x − 6 = x − 54
Answer: x = −6
- Subtract 1x from both sides: 8x − 6 = −54
- Add 6: 8x = −48
- Divide by 8: x = −6
3.3(x + 5) = −9
Answer: x = −8
- Expand: 3x + 15 = −9
- Subtract 15: 3x = −24
- Divide by 3: x = −8
4.5(x − 2) = −15
Answer: x = −1
- Expand: 5x − 10 = −15
- Add 10: 5x = −5
- Divide by 5: x = −1
5.8x − 3 = 6x + 7
Answer: x = 5
- Subtract 6x from both sides: 2x − 3 = 7
- Add 3: 2x = 10
- Divide by 2: x = 5
6.9x + 2 = 3x − 28
Answer: x = −5
- Subtract 3x from both sides: 6x + 2 = −28
- Subtract 2: 6x = −30
- Divide by 6: x = −5
7.2(x − 1) = −14
Answer: x = −6
- Expand: 2x − 2 = −14
- Add 2: 2x = −12
- Divide by 2: x = −6
8.5x − 4 = 3x − 6
Answer: x = −1
- Subtract 3x from both sides: 2x − 4 = −6
- Add 4: 2x = −2
- Divide by 2: x = −1
9.6(x − 3) = −60
Answer: x = −7
- Expand: 6x − 18 = −60
- Add 18: 6x = −42
- Divide by 6: x = −7
10.2(x − 4) = −4
Answer: x = 2
- Expand: 2x − 8 = −4
- Add 8: 2x = 4
- Divide by 2: x = 2
11.4x − 3 = x + 33
Answer: x = 12
- Subtract 1x from both sides: 3x − 3 = 33
- Add 3: 3x = 36
- Divide by 3: x = 12
12.3(x − 8) = −48
Answer: x = −8
- Expand: 3x − 24 = −48
- Add 24: 3x = −24
- Divide by 3: x = −8
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.
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