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Year 8 Mathematics · Solving simple equations

Name: ______________________

Date: ____________

1. Solve x + 9 = 14.
- ☐ (a) x = 23
- ☐ (b) x = 5
- ☐ (c) x = −5
- ☐ (d) x = 9
2. Solve 4m = 28.
- ☐ (a) m = 7
- ☐ (b) m = 24
- ☐ (c) m = 32
- ☐ (d) m = 112
3. Ali solves 2x + 5 = 17. His first step is to subtract 5 from both sides. Which equation does he get?
- ☐ (a) 2x = 12
- ☐ (b) 2x = 22
- ☐ (c) x + 5 = 12
- ☐ (d) 2x = 17
4. Which value of y is the solution of 3y − 2 = 13?
- ☐ (a) y = 3
- ☐ (b) y = 4
- ☐ (c) y = 5
- ☐ (d) y = 6
5. Solve y − 6 = 11.
6. Solve 5x + 3 = 38.
7. Solve a ÷ 3 − 1 = 4.
8. I think of a number, multiply it by 4 and then add 6. The answer is 34. What number did I think of?

Answer sheet

1. x = 5 — Subtract 9 from both sides: x = 14 − 9 = 5.
2. m = 7 — Divide both sides by 4: m = 28 ÷ 4 = 7.
3. 2x = 12 — 2x + 5 − 5 = 17 − 5, so 2x = 12. (Then x = 6.)
4. y = 5 — Substitute: 3 × 5 − 2 = 15 − 2 = 13. ✓ The other values do not give 13.
5. y = 17 — Add 6 to both sides: y = 11 + 6 = 17. Check: 17 − 6 = 11.
6. x = 7 — Subtract 3: 5x = 35. Divide by 5: x = 7. Check: 5 × 7 + 3 = 38.
7. a = 15 — Add 1: a ÷ 3 = 5. Multiply by 3: a = 15. Check: 15 ÷ 3 − 1 = 5 − 1 = 4.
8. 7 — Write 4n + 6 = 34. Subtract 6: 4n = 28. Divide by 4: n = 7. Check: 4 × 7 + 6 = 34.