Let's solve each equation step by step. The goal is to isolate the variable $ x $ on one side of the equation.
---
1. $ 3x - 18 = 0 $
Add 18 to both sides:
$$
3x = 18
$$
Divide both sides by 3:
$$
x = 6
$$
✔ Answer: $ x = 6 $
---
2. $ 4x - 12 = 0 $
Add 12 to both sides:
$$
4x = 12
$$
Divide by 4:
$$
x = 3
$$
✔ Answer: $ x = 3 $
---
3. $ 5x + 20 = -14 $
Subtract 20 from both sides:
$$
5x = -34
$$
Divide by 5:
$$
x = -\frac{34}{5} = -6.8
$$
✔ Answer: $ x = -\frac{34}{5} $ or $ -6.8 $
---
4. $ 7x - 6 = -20 $
Add 6 to both sides:
$$
7x = -14
$$
Divide by 7:
$$
x = -2
$$
✔ Answer: $ x = -2 $
---
5. $ 6x = -24 $
Divide by 6:
$$
x = -4
$$
✔ Answer: $ x = -4 $
---
6. $ 3x - 12 = 0 $
Add 12 to both sides:
$$
3x = 12
$$
Divide by 3:
$$
x = 4
$$
✔ Answer: $ x = 4 $
---
7. $ 8x - 12 = 12 $
Add 12 to both sides:
$$
8x = 24
$$
Divide by 8:
$$
x = 3
$$
✔ Answer: $ x = 3 $
---
8. $ 9x + 20 = -7 $
Subtract 20 from both sides:
$$
9x = -27
$$
Divide by 9:
$$
x = -3
$$
✔ Answer: $ x = -3 $
---
9. $ 2x - 6 = -20 $
Add 6 to both sides:
$$
2x = -14
$$
Divide by 2:
$$
x = -7
$$
✔ Answer: $ x = -7 $
---
10. $ 5x - 4 = -24 $
Add 4 to both sides:
$$
5x = -20
$$
Divide by 5:
$$
x = -4
$$
✔ Answer: $ x = -4 $
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1. | $ x = 6 $ |
| 2. | $ x = 3 $ |
| 3. | $ x = -\frac{34}{5} $ or $ -6.8 $ |
| 4. | $ x = -2 $ |
| 5. | $ x = -4 $ |
| 6. | $ x = 4 $ |
| 7. | $ x = 3 $ |
| 8. | $ x = -3 $ |
| 9. | $ x = -7 $ |
| 10. | $ x = -4 $ |
> ⚠️ Note: There appears to be a typo in the worksheet — problems 3 and 4 are listed twice, with different equations. I've solved all unique equations as numbered.
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Parent Tip: Review the logic above to help your child master the concept of algebra equations worksheets.
