Solve equations with variables on both sides in this algebra practice worksheet.

Let's solve each equation step by step. These are linear equations with variables on both sides. The goal is to isolate the variable $ x $ on one side of the equation.

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1. $ 7x - 3 = 3x + 8 $

Step 1: Subtract $ 3x $ from both sides:
$$
7x - 3x - 3 = 8 \Rightarrow 4x - 3 = 8
$$

Step 2: Add 3 to both sides:
$$
4x = 11
$$

Step 3: Divide by 4:
$$
x = \frac{11}{4}
$$

✔ Answer: $ x = \frac{11}{4} $

---

2. $ 5x + 4 = 2x + 9 $

Step 1: Subtract $ 2x $ from both sides:
$$
3x + 4 = 9
$$

Step 2: Subtract 4:
$$
3x = 5
$$

Step 3: Divide by 3:
$$
x = \frac{5}{3}
$$

✔ Answer: $ x = \frac{5}{3} $

---

3. $ 6x - 2 = x + 8 $

Step 1: Subtract $ x $ from both sides:
$$
5x - 2 = 8
$$

Step 2: Add 2:
$$
5x = 10
$$

Step 3: Divide by 5:
$$
x = 2
$$

✔ Answer: $ x = 2 $

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4. $ 8x + 1 = 3x + 2 $

Step 1: Subtract $ 3x $:
$$
5x + 1 = 2
$$

Step 2: Subtract 1:
$$
5x = 1
$$

Step 3: Divide by 5:
$$
x = \frac{1}{5}
$$

✔ Answer: $ x = \frac{1}{5} $

---

5. $ 7x - 10 = 3x - 8 $

Step 1: Subtract $ 3x $:
$$
4x - 10 = -8
$$

Step 2: Add 10:
$$
4x = 2
$$

Step 3: Divide by 4:
$$
x = \frac{1}{2}
$$

✔ Answer: $ x = \frac{1}{2} $

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6. $ 5x - 12 = 2x - 6 $

Step 1: Subtract $ 2x $:
$$
3x - 12 = -6
$$

Step 2: Add 12:
$$
3x = 6
$$

Step 3: Divide by 3:
$$
x = 2
$$

✔ Answer: $ x = 2 $

---

7. $ 4x - 23 = x - 7 $

Step 1: Subtract $ x $:
$$
3x - 23 = -7
$$

Step 2: Add 23:
$$
3x = 16
$$

Step 3: Divide by 3:
$$
x = \frac{16}{3}
$$

✔ Answer: $ x = \frac{16}{3} $

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8. $ 8x - 8 = 3x - 2 $

Step 1: Subtract $ 3x $:
$$
5x - 8 = -2
$$

Step 2: Add 8:
$$
5x = 6
$$

Step 3: Divide by 5:
$$
x = \frac{6}{5}
$$

✔ Answer: $ x = \frac{6}{5} $

---

9. $ 11x + 7 = 6x + 7 $

Step 1: Subtract $ 6x $:
$$
5x + 7 = 7
$$

Step 2: Subtract 7:
$$
5x = 0
$$

Step 3: Divide by 5:
$$
x = 0
$$

✔ Answer: $ x = 0 $

---

10. $ 9x + 8 = 10 $

Step 1: Subtract 8:
$$
9x = 2
$$

Step 2: Divide by 9:
$$
x = \frac{2}{9}
$$

✔ Answer: $ x = \frac{2}{9} $

---

11. $ 5 + 3x = x + 8 $

Step 1: Subtract $ x $:
$$
5 + 2x = 8
$$

Step 2: Subtract 5:
$$
2x = 3
$$

Step 3: Divide by 2:
$$
x = \frac{3}{2}
$$

✔ Answer: $ x = \frac{3}{2} $

---

12. $ 4 + 7x = x + 5 $

Step 1: Subtract $ x $:
$$
4 + 6x = 5
$$

Step 2: Subtract 4:
$$
6x = 1
$$

Step 3: Divide by 6:
$$
x = \frac{1}{6}
$$

✔ Answer: $ x = \frac{1}{6} $

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13. $ 6x - 8 = 4 - 2x $

Step 1: Add $ 2x $ to both sides:
$$
8x - 8 = 4
$$

Step 2: Add 8:
$$
8x = 12
$$

Step 3: Divide by 8:
$$
x = \frac{12}{8} = \frac{3}{2}
$$

✔ Answer: $ x = \frac{3}{2} $

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14. $ 5x + 1 = 7 - 2x $

Step 1: Add $ 2x $:
$$
7x + 1 = 7
$$

Step 2: Subtract 1:
$$
7x = 6
$$

Step 3: Divide by 7:
$$
x = \frac{6}{7}
$$

✔ Answer: $ x = \frac{6}{7} $

---

15. $ 6x - 3 = 1 - x $

Step 1: Add $ x $:
$$
7x - 3 = 1
$$

Step 2: Add 3:
$$
7x = 4
$$

Step 3: Divide by 7:
$$
x = \frac{4}{7}
$$

✔ Answer: $ x = \frac{4}{7} $

---

16. $ 3x - 10 = 2x - 3 $

Step 1: Subtract $ 2x $:
$$
x - 10 = -3
$$

Step 2: Add 10:
$$
x = 7
$$

✔ Answer: $ x = 7 $

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17. $ 5x + 1 = 6 - 3x $

Step 1: Add $ 3x $:
$$
8x + 1 = 6
$$

Step 2: Subtract 1:
$$
8x = 5
$$

Step 3: Divide by 8:
$$
x = \frac{5}{8}
$$

✔ Answer: $ x = \frac{5}{8} $

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18. $ 11x - 20 = 10x - 15 $

Step 1: Subtract $ 10x $:
$$
x - 20 = -15
$$

Step 2: Add 20:
$$
x = 5
$$

✔ Answer: $ x = 5 $

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19. $ 6 + 2x = 8 - 3x $

Step 1: Add $ 3x $:
$$
6 + 5x = 8
$$

Step 2: Subtract 6:
$$
5x = 2
$$

Step 3: Divide by 5:
$$
x = \frac{2}{5}
$$

✔ Answer: $ x = \frac{2}{5} $

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20. $ 7 + x = 9 - 5x $

Step 1: Add $ 5x $:
$$
7 + 6x = 9
$$

Step 2: Subtract 7:
$$
6x = 2
$$

Step 3: Divide by 6:
$$
x = \frac{1}{3}
$$

✔ Answer: $ x = \frac{1}{3} $

---

21. $ 3y - 7 = y + 1 $

Note: This equation uses $ y $, not $ x $. Let’s solve for $ y $.

Step 1: Subtract $ y $:
$$
2y - 7 = 1
$$

Step 2: Add 7:
$$
2y = 8
$$

Step 3: Divide by 2:
$$
y = 4
$$

✔ Answer: $ y = 4 $

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✔ Final Answers:

| Equation | Solution |
|--------|---------|
| 1 | $ x = \frac{11}{4} $ |
| 2 | $ x = \frac{5}{3} $ |
| 3 | $ x = 2 $ |
| 4 | $ x = \frac{1}{5} $ |
| 5 | $ x = \frac{1}{2} $ |
| 6 | $ x = 2 $ |
| 7 | $ x = \frac{16}{3} $ |
| 8 | $ x = \frac{6}{5} $ |
| 9 | $ x = 0 $ |
| 10 | $ x = \frac{2}{9} $ |
| 11 | $ x = \frac{3}{2} $ |
| 12 | $ x = \frac{1}{6} $ |
| 13 | $ x = \frac{3}{2} $ |
| 14 | $ x = \frac{6}{7} $ |
| 15 | $ x = \frac{4}{7} $ |
| 16 | $ x = 7 $ |
| 17 | $ x = \frac{5}{8} $ |
| 18 | $ x = 5 $ |
| 19 | $ x = \frac{2}{5} $ |
| 20 | $ x = \frac{1}{3} $ |
| 21 | $ y = 4 $ |

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