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Year 8 Mathematics · Solving linear equations

Name: ______________________

Date: ____________

1. Solve x + 9 = 4.
- ☐ (a) x = 13
- ☐ (b) x = −5
- ☐ (c) x = 5
- ☐ (d) x = −13
2. Solve 4x = 28.
- ☐ (a) x = 24
- ☐ (b) x = 32
- ☐ (c) x = 112
- ☐ (d) x = 7
3. Which is a correct first step for solving x/3 − 2 = 5?
- ☐ (a) Add 2 to both sides
- ☐ (b) Subtract 2 from the left side only
- ☐ (c) Divide both sides by 3
- ☐ (d) Add 5 to both sides
4. Solve 2(x + 4) = 18.
- ☐ (a) x = 7
- ☐ (b) x = 5
- ☐ (c) x = 9
- ☐ (d) x = 10
5. Which equation has the solution x = 3?
- ☐ (a) 3x − 1 = 10
- ☐ (b) x/3 = 3
- ☐ (c) 2x + 1 = 7
- ☐ (d) 5 − x = 8
6. Solve 6x − 5 = 31.
7. Solve 7x + 2 = 3x + 18.
8. Mia thinks of a number. She multiplies it by 4 and then subtracts 6. Her answer is 30. What was her number?

Answer sheet

1. x = −5 — Subtract 9 from both sides: x = 4 − 9 = −5.
2. x = 7 — Divide both sides by 4: x = 28 ÷ 4 = 7.
3. Add 2 to both sides — Adding 2 to both sides undoes the subtraction and keeps the equation balanced: x/3 = 7, so x = 21.
4. x = 5 — Divide both sides by 2 to get x + 4 = 9, then subtract 4 to get x = 5.
5. 2x + 1 = 7 — Substitute x = 3: 2 × 3 + 1 = 7, which is true. The others give 8 ≠ 10, 1 ≠ 3 and 2 ≠ 8.
6. x = 6 — Add 5 to both sides (6x = 36), then divide by 6 (x = 6).
7. x = 4 — Subtract 3x from both sides (4x + 2 = 18), subtract 2 (4x = 16), then divide by 4 (x = 4).
8. 9 — Write the equation 4n − 6 = 30. Add 6 to get 4n = 36, then divide by 4 to get n = 9.