Algebra worksheet featuring equations to solve for x, with space for answers.

Let's solve each equation step by step. We'll isolate the variable $ x $ in each case using algebraic operations.

---

1. $ 3x + 3 = 57 $

Subtract 3 from both sides:
$$
3x = 57 - 3 = 54
$$

Divide both sides by 3:
$$
x = \frac{54}{3} = 18
$$

✔ Answer: $ x = 18 $

---

2. $ x \div 4 + 10 = 21 $

Subtract 10 from both sides:
$$
\frac{x}{4} = 21 - 10 = 11
$$

Multiply both sides by 4:
$$
x = 11 \times 4 = 44
$$

✔ Answer: $ x = 44 $

---

3. $ 3x - 2 = 4 $

Add 2 to both sides:
$$
3x = 4 + 2 = 6
$$

Divide both sides by 3:
$$
x = \frac{6}{3} = 2
$$

✔ Answer: $ x = 2 $

---

4. $ x \div 11 + 12 = 22 $

Subtract 12 from both sides:
$$
\frac{x}{11} = 22 - 12 = 10
$$

Multiply both sides by 11:
$$
x = 10 \times 11 = 110
$$

✔ Answer: $ x = 110 $

---

5. $ 9x + 1 = 100 $

Subtract 1 from both sides:
$$
9x = 100 - 1 = 99
$$

Divide both sides by 9:
$$
x = \frac{99}{9} = 11
$$

✔ Answer: $ x = 11 $

---

6. $ 7x - 16 = 68 $

Add 16 to both sides:
$$
7x = 68 + 16 = 84
$$

Divide both sides by 7:
$$
x = \frac{84}{7} = 12
$$

✔ Answer: $ x = 12 $

---

7. $ x \div 6 + 18 = 22 $

Subtract 18 from both sides:
$$
\frac{x}{6} = 22 - 18 = 4
$$

Multiply both sides by 6:
$$
x = 4 \times 6 = 24
$$

✔ Answer: $ x = 24 $

---

8. $ x \div 11 - 1 = 10 $

Add 1 to both sides:
$$
\frac{x}{11} = 10 + 1 = 11
$$

Multiply both sides by 11:
$$
x = 11 \times 11 = 121
$$

✔ Answer: $ x = 121 $

---

9. $ x \div 9 + 13 = 20 $

Subtract 13 from both sides:
$$
\frac{x}{9} = 20 - 13 = 7
$$

Multiply both sides by 9:
$$
x = 7 \times 9 = 63
$$

✔ Answer: $ x = 63 $

---

10. $ 2x - 1 = 19 $

Add 1 to both sides:
$$
2x = 19 + 1 = 20
$$

Divide both sides by 2:
$$
x = \frac{20}{2} = 10
$$

✔ Answer: $ 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 $ |

---

🔍 Summary of Strategy:

To solve for $ x $, we use inverse operations:
- Undo addition/subtraction first.
- Then undo multiplication/division.
- Always perform the same operation on both sides to keep the equation balanced.

Let me know if you'd like these steps written out neatly for a worksheet!