Let's solve each equation step by step for $ x $. We'll use algebraic methods: isolate the variable on one side of the equation using inverse operations.
---
1. $ 3x + 3 = 57 $
- Subtract 3 from both sides:
$$
3x = 57 - 3 = 54
$$
- Divide both sides by 3:
$$
x = \frac{54}{3} = 18
$$
✔ $ x = 18 $
---
2. $ x \div 4 + 10 = 21 $
- Subtract 10 from both sides:
$$
x \div 4 = 21 - 10 = 11
$$
- Multiply both sides by 4:
$$
x = 11 \times 4 = 44
$$
✔ $ x = 44 $
---
3. $ 3x - 2 = 4 $
- Add 2 to both sides:
$$
3x = 4 + 2 = 6
$$
- Divide by 3:
$$
x = \frac{6}{3} = 2
$$
✔ $ x = 2 $
---
4. $ x \div 11 + 12 = 22 $
- Subtract 12 from both sides:
$$
x \div 11 = 22 - 12 = 10
$$
- Multiply by 11:
$$
x = 10 \times 11 = 110
$$
✔ $ x = 110 $
---
5. $ 9x + 1 = 100 $
- Subtract 1:
$$
9x = 100 - 1 = 99
$$
- Divide by 9:
$$
x = \frac{99}{9} = 11
$$
✔ $ x = 11 $
---
6. $ 7x - 16 = 68 $
- Add 16:
$$
7x = 68 + 16 = 84
$$
- Divide by 7:
$$
x = \frac{84}{7} = 12
$$
✔ $ x = 12 $
---
7. $ x \div 6 + 18 = 22 $
- Subtract 18:
$$
x \div 6 = 22 - 18 = 4
$$
- Multiply by 6:
$$
x = 4 \times 6 = 24
$$
✔ $ x = 24 $
---
8. $ x \div 11 - 1 = 10 $
- Add 1:
$$
x \div 11 = 10 + 1 = 11
$$
- Multiply by 11:
$$
x = 11 \times 11 = 121
$$
✔ $ x = 121 $
---
9. $ x \div 9 + 13 = 20 $
- Subtract 13:
$$
x \div 9 = 20 - 13 = 7
$$
- Multiply by 9:
$$
x = 7 \times 9 = 63
$$
✔ $ x = 63 $
---
10. $ 2x - 1 = 19 $
- Add 1:
$$
2x = 19 + 1 = 20
$$
- Divide by 2:
$$
x = \frac{20}{2} = 10
$$
✔ $ x = 10 $
---
✔ Final Answers:
| Equation | Solution |
|--------|---------|
| $ 3x + 3 = 57 $ | $ x = 18 $ |
| $ x \div 4 + 10 = 21 $ | $ x = 44 $ |
| $ 3x - 2 = 4 $ | $ x = 2 $ |
| $ x \div 11 + 12 = 22 $ | $ x = 110 $ |
| $ 9x + 1 = 100 $ | $ x = 11 $ |
| $ 7x - 16 = 68 $ | $ x = 12 $ |
| $ x \div 6 + 18 = 22 $ | $ x = 24 $ |
| $ x \div 11 - 1 = 10 $ | $ x = 121 $ |
| $ x \div 9 + 13 = 20 $ | $ x = 63 $ |
| $ 2x - 1 = 19 $ | $ x = 10 $ |
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Parent Tip: Review the logic above to help your child master the concept of solving 2 step equations worksheet.
