This worksheet provides 15 practice problems for students to solve one-variable linear equations in the form ax+b=c.

Let's solve each of these one-variable linear equations step by step. The general form is $ ax + b = c $, and we'll isolate the variable $ x $ using algebraic operations.

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1. $ 4x + 7 = 43 $

- Subtract 7 from both sides:
$ 4x = 43 - 7 = 36 $
- Divide by 4:
$ x = \frac{36}{4} = 9 $

✔ Answer: $ x = 9 $

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2. $ 2x - 3 = 3 $

- Add 3 to both sides:
$ 2x = 3 + 3 = 6 $
- Divide by 2:
$ x = \frac{6}{2} = 3 $

✔ Answer: $ x = 3 $

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3. $ 6x + 6 = 36 $

- Subtract 6:
$ 6x = 36 - 6 = 30 $
- Divide by 6:
$ x = \frac{30}{6} = 5 $

✔ Answer: $ x = 5 $

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4. $ 3x + 2 = 17 $

- Subtract 2:
$ 3x = 17 - 2 = 15 $
- Divide by 3:
$ x = \frac{15}{3} = 5 $

✔ Answer: $ x = 5 $

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5. $ 2x + 5 = 9 $

- Subtract 5:
$ 2x = 9 - 5 = 4 $
- Divide by 2:
$ x = \frac{4}{2} = 2 $

✔ Answer: $ x = 2 $

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6. $ 6x - 5 = 7 $

- Add 5:
$ 6x = 7 + 5 = 12 $
- Divide by 6:
$ x = \frac{12}{6} = 2 $

✔ Answer: $ x = 2 $

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7. $ 4x + 4 = 16 $

- Subtract 4:
$ 4x = 16 - 4 = 12 $
- Divide by 4:
$ x = \frac{12}{4} = 3 $

✔ Answer: $ x = 3 $

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8. $ 2x + 5 = 19 $

- Subtract 5:
$ 2x = 19 - 5 = 14 $
- Divide by 2:
$ x = \frac{14}{2} = 7 $

✔ Answer: $ x = 7 $

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9. $ 4x + 2 = 6 $

- Subtract 2:
$ 4x = 6 - 2 = 4 $
- Divide by 4:
$ x = \frac{4}{4} = 1 $

✔ Answer: $ x = 1 $

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10. $ 2x - 3 = 3 $

- Add 3:
$ 2x = 3 + 3 = 6 $
- Divide by 2:
$ x = \frac{6}{2} = 3 $

✔ Answer: $ x = 3 $

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11. $ 4x - 4 = 20 $

- Add 4:
$ 4x = 20 + 4 = 24 $
- Divide by 4:
$ x = \frac{24}{4} = 6 $

✔ Answer: $ x = 6 $

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12. $ 3x - 4 = 17 $

- Add 4:
$ 3x = 17 + 4 = 21 $
- Divide by 3:
$ x = \frac{21}{3} = 7 $

✔ Answer: $ x = 7 $

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13. $ 5x - 7 = 8 $

- Add 7:
$ 5x = 8 + 7 = 15 $
- Divide by 5:
$ x = \frac{15}{5} = 3 $

✔ Answer: $ x = 3 $

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14. $ 2x + 2 = 12 $

- Subtract 2:
$ 2x = 12 - 2 = 10 $
- Divide by 2:
$ x = \frac{10}{2} = 5 $

✔ Answer: $ x = 5 $

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15. $ 2x - 7 = 11 $

- Add 7:
$ 2x = 11 + 7 = 18 $
- Divide by 2:
$ x = \frac{18}{2} = 9 $

✔ Answer: $ x = 9 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ x = 9 $ |
| 2 | $ x = 3 $ |
| 3 | $ x = 5 $ |
| 4 | $ x = 5 $ |
| 5 | $ x = 2 $ |
| 6 | $ x = 2 $ |
| 7 | $ x = 3 $ |
| 8 | $ x = 7 $ |
| 9 | $ x = 1 $ |
| 10 | $ x = 3 $ |
| 11 | $ x = 6 $ |
| 12 | $ x = 7 $ |
| 13 | $ x = 3 $ |
| 14 | $ x = 5 $ |
| 15 | $ x = 9 $ |

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🔍 Summary of Steps:

To solve any equation $ ax + b = c $:
1. Move constants to the other side (add or subtract).
2. Isolate the variable term.
3. Divide by the coefficient of $ x $.

This method works for all linear one-variable equations.

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