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Ignition Learning — Activity Sheet

Solving multi-step equations

Mathematics · Year 9

Name: ______________________Date: ____________

Multi-step equations require more than one operation to solve, but the same rule always applies: whatever you do to one side, do to the other, working step by step to isolate the unknown. A common approach is to deal with addition/subtraction first, then multiplication/division, and to expand any brackets before starting.

Example

Solve 3x + 5 = 20: subtract 5 from both sides → 3x = 15; divide both sides by 3 → x = 5. Solve 2(x + 3) = 16: expand → 2x + 6 = 16; subtract 6 → 2x = 10; divide by 2 → x = 5.

Key terms

Isolate:: To get the unknown by itself on one side of an equation.
Inverse operation:: The operation that undoes another, used to isolate the unknown.

Questions

1. Solve: 2x + 3 = 11
- 3
- 4
- 5
- 7
2. Solve: 3x − 2 = 10
- 3
- 4
- 5
- 6
3. Solve: x/2 + 1 = 5
- 4
- 6
- 8
- 10
4. Solve: 5x = 25
- 4
- 5
- 6
- 20
5. Solve: 4x + 1 = 17
- 3
- 4
- 5
- 6
6. The first step to solve 2x + 3 = 11 is usually to:
- Subtract 3 from both sides
- Divide by 3
- Add 11
- Multiply by 2
7. Solve: x − 7 = 3
- 4
- 10
- −4
- 21
8. Solve: 3x + 5 = 20
- 3
- 5
- 15
- 25
9. Solve: 2(x + 3) = 16
- 3
- 5
- 8
- 10
10. Solve: 5x − 4 = 3x + 10
- 3
- 5
- 7
- 9
11. Solve: 4(x − 2) = 20
- 5
- 6
- 7
- 8
12. Solve: 2x + 7 = x + 15
- 6
- 7
- 8
- 9
13. Solve: 3(x + 1) − 2 = 10
- 3
- 4
- 5
- 6
14. Solve: 6x − 3 = 3x + 12
- 3
- 4
- 5
- 6
15. Solve: 2(3x − 1) = 4x + 8
- 3
- 4
- 5
- 6
16. Solve: 5(x + 2) − 3(x − 1) = 25
- 5
- 6
- 7
- 8
17. A phone plan costs $20 plus $0.50 per gigabyte. If the bill was $35, solve for the gigabytes used (g): 20 + 0.5g = 35
- 20
- 25
- 30
- 35
18. Solve: 4(2x − 1) = 3(x + 5)
- 3.4
- 3.8
- 4.0
- 2.6
19. Two numbers differ by 8, and their sum is 26. Using x for the smaller number: x + (x + 8) = 26. Solve for x.
- 7
- 8
- 9
- 10
20. Solve: 3(x − 4) + 2(x + 1) = 21
- 5
- 5.4
- 5.8
- 6
21. Solve: 7x − 2(x + 3) = 19
- 4
- 5
- 6
- 7

Answer key (parent copy)

1. 4
2. 4
3. 8
4. 5
5. 5
6. Subtract 3 from both sides
7. 10
8. 5
9. 5
10. 7
11. 7
12. 8
13. 3
14. 5
15. 4
16. 6
17. 30
18. 3.8
19. 9
20. 5.8
21. 5