Comprehensive worksheet featuring 40 algebraic equations for students to solve, ranging from basic addition to two-step problems.

Let's solve each of these algebraic equations step by step. The goal is to isolate the variable on one side of the equation.

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1. $ x + 5 = 9 $

Subtract 5 from both sides:
$ x = 9 - 5 = 4 $
✔ $ x = 4 $

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2. $ x + 7 = 15 $

Subtract 7:
$ x = 15 - 7 = 8 $
✔ $ x = 8 $

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3. $ x + 1 = 8 $

Subtract 1:
$ x = 8 - 1 = 7 $
✔ $ x = 7 $

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4. $ x + 11 = 21 $

Subtract 11:
$ x = 21 - 11 = 10 $
✔ $ x = 10 $

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5. $ x + 6 = 4 $

Subtract 6:
$ x = 4 - 6 = -2 $
✔ $ x = -2 $

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6. $ x + 4 = 4 $

Subtract 4:
$ x = 4 - 4 = 0 $
✔ $ x = 0 $

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7. $ y + 20 = 32 $

Subtract 20:
$ y = 32 - 20 = 12 $
✔ $ y = 12 $

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8. $ y + 12 = 30 $

Subtract 12:
$ y = 30 - 12 = 18 $
✔ $ y = 18 $

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9. $ t + 8 = 101 $

Subtract 8:
$ t = 101 - 8 = 93 $
✔ $ t = 93 $

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10. $ r + 0.5 = 9 $

Subtract 0.5:
$ r = 9 - 0.5 = 8.5 $
✔ $ r = 8.5 $

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11. $ x - 1 = 10 $

Add 1:
$ x = 10 + 1 = 11 $
✔ $ x = 11 $

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12. $ x - 5 = 2 $

Add 5:
$ x = 2 + 5 = 7 $
✔ $ x = 7 $

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13. $ x - 8 = 20 $

Add 8:
$ x = 20 + 8 = 28 $
✔ $ x = 28 $

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14. $ x - 9 = -3 $

Add 9:
$ x = -3 + 9 = 6 $
✔ $ x = 6 $

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15. $ x - 3 = 21 $

Add 3:
$ x = 21 + 3 = 24 $
✔ $ x = 24 $

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16. $ x - 7 = 4 $

Add 7:
$ x = 4 + 7 = 11 $
✔ $ x = 11 $

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17. $ y - 10 = 34 $

Add 10:
$ y = 34 + 10 = 44 $
✔ $ y = 44 $

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18. $ t - 52 = 11 $

Add 52:
$ t = 11 + 52 = 63 $
✔ $ t = 63 $

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19. $ t - 3.5 = 9 $

Add 3.5:
$ t = 9 + 3.5 = 12.5 $
✔ $ t = 12.5 $

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20. $ p - 21 = -4 $

Add 21:
$ p = -4 + 21 = 17 $
✔ $ p = 17 $

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21. $ 2x = 12 $

Divide by 2:
$ x = 12 ÷ 2 = 6 $
✔ $ x = 6 $

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22. $ 5x = 15 $

Divide by 5:
$ x = 15 ÷ 5 = 3 $
✔ $ x = 3 $

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23. $ 3x = -6 $

Divide by 3:
$ x = -6 ÷ 3 = -2 $
✔ $ x = -2 $

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24. $ 8x = 32 $

Divide by 8:
$ x = 32 ÷ 8 = 4 $
✔ $ x = 4 $

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25. $ 4x = 14 $

Divide by 4:
$ x = 14 ÷ 4 = 3.5 $
✔ $ x = 3.5 $ or $ \frac{7}{2} $

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26. $ 9x = -27 $

Divide by 9:
$ x = -27 ÷ 9 = -3 $
✔ $ x = -3 $

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27. $ 6x = 31 $

Divide by 6:
$ x = 31 ÷ 6 ≈ 5.1667 $
✔ $ x = \frac{31}{6} $ or $ 5\frac{1}{6} $

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28. $ 11x = 88 $

Divide by 11:
$ x = 88 ÷ 11 = 8 $
✔ $ x = 8 $

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29. $ 3y = 17 $

Divide by 3:
$ y = 17 ÷ 3 ≈ 5.6667 $
✔ $ y = \frac{17}{3} $ or $ 5\frac{2}{3} $

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30. $ 3.5p = 10.5 $

Divide by 3.5:
$ p = 10.5 ÷ 3.5 = 3 $
✔ $ p = 3 $

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31. $ 2x + 1 = 13 $

Subtract 1: $ 2x = 12 $
Divide by 2: $ x = 6 $
✔ $ x = 6 $

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32. $ 5x - 2 = 23 $

Add 2: $ 5x = 25 $
Divide by 5: $ x = 5 $
✔ $ x = 5 $

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33. $ 8t + 3 = 43 $

Subtract 3: $ 8t = 40 $
Divide by 8: $ t = 5 $
✔ $ t = 5 $

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34. $ 4x + 10 = 42 $

Subtract 10: $ 4x = 32 $
Divide by 4: $ x = 8 $
✔ $ x = 8 $

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35. $ 7x - 2 = 65 $

Add 2: $ 7x = 67 $
Divide by 7: $ x = 67 ÷ 7 ≈ 9.5714 $
✔ $ x = \frac{67}{7} $ or $ 9\frac{4}{7} $

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36. $ 3y + 4 = -11 $

Subtract 4: $ 3y = -15 $
Divide by 3: $ y = -5 $
✔ $ y = -5 $

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37. $ 6t + 7 = 28 $

Subtract 7: $ 6t = 21 $
Divide by 6: $ t = 21 ÷ 6 = 3.5 $
✔ $ t = 3.5 $ or $ \frac{7}{2} $

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38. $ 7x - 1 = 25 $

Add 1: $ 7x = 26 $
Divide by 7: $ x = 26 ÷ 7 ≈ 3.7143 $
✔ $ x = \frac{26}{7} $ or $ 3\frac{5}{7} $

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39. $ 3p - 4 = -2 $

Add 4: $ 3p = 2 $
Divide by 3: $ p = \frac{2}{3} $
✔ $ p = \frac{2}{3} $

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40. $ 12q + 3 = 36 $

Subtract 3: $ 12q = 33 $
Divide by 12: $ q = 33 ÷ 12 = 2.75 $
✔ $ q = \frac{11}{4} $ or $ 2\frac{3}{4} $

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✔ Final Answers:

| No. | Equation | Answer |
|-----|---------------------|----------------|
| 1 | $ x + 5 = 9 $ | $ x = 4 $ |
| 2 | $ x + 7 = 15 $ | $ x = 8 $ |
| 3 | $ x + 1 = 8 $ | $ x = 7 $ |
| 4 | $ x + 11 = 21 $ | $ x = 10 $ |
| 5 | $ x + 6 = 4 $ | $ x = -2 $ |
| 6 | $ x + 4 = 4 $ | $ x = 0 $ |
| 7 | $ y + 20 = 32 $ | $ y = 12 $ |
| 8 | $ y + 12 = 30 $ | $ y = 18 $ |
| 9 | $ t + 8 = 101 $ | $ t = 93 $ |
| 10 | $ r + 0.5 = 9 $ | $ r = 8.5 $ |
| 11 | $ x - 1 = 10 $ | $ x = 11 $ |
| 12 | $ x - 5 = 2 $ | $ x = 7 $ |
| 13 | $ x - 8 = 20 $ | $ x = 28 $ |
| 14 | $ x - 9 = -3 $ | $ x = 6 $ |
| 15 | $ x - 3 = 21 $ | $ x = 24 $ |
| 16 | $ x - 7 = 4 $ | $ x = 11 $ |
| 17 | $ y - 10 = 34 $ | $ y = 44 $ |
| 18 | $ t - 52 = 11 $ | $ t = 63 $ |
| 19 | $ t - 3.5 = 9 $ | $ t = 12.5 $ |
| 20 | $ p - 21 = -4 $ | $ p = 17 $ |
| 21 | $ 2x = 12 $ | $ x = 6 $ |
| 22 | $ 5x = 15 $ | $ x = 3 $ |
| 23 | $ 3x = -6 $ | $ x = -2 $ |
| 24 | $ 8x = 32 $ | $ x = 4 $ |
| 25 | $ 4x = 14 $ | $ x = 3.5 $ |
| 26 | $ 9x = -27 $ | $ x = -3 $ |
| 27 | $ 6x = 31 $ | $ x = \frac{31}{6} $ |
| 28 | $ 11x = 88 $ | $ x = 8 $ |
| 29 | $ 3y = 17 $ | $ y = \frac{17}{3} $ |
| 30 | $ 3.5p = 10.5 $ | $ p = 3 $ |
| 31 | $ 2x + 1 = 13 $ | $ x = 6 $ |
| 32 | $ 5x - 2 = 23 $ | $ x = 5 $ |
| 33 | $ 8t + 3 = 43 $ | $ t = 5 $ |
| 34 | $ 4x + 10 = 42 $ | $ x = 8 $ |
| 35 | $ 7x - 2 = 65 $ | $ x = \frac{67}{7} $ |
| 36 | $ 3y + 4 = -11 $ | $ y = -5 $ |
| 37 | $ 6t + 7 = 28 $ | $ t = 3.5 $ |
| 38 | $ 7x - 1 = 25 $ | $ x = \frac{26}{7} $ |
| 39 | $ 3p - 4 = -2 $ | $ p = \frac{2}{3} $ |
| 40 | $ 12q + 3 = 36 $ | $ q = \frac{11}{4} $ |

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