One-step equations worksheet for solving algebraic expressions, designed for educational use.

Let's solve each of these one-step equations step by step. A one-step equation is an equation that can be solved in a single operation (addition, subtraction, multiplication, or division).

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Solving One-Step Equations

We will isolate the variable on one side of the equation using inverse operations.

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#### 1. $ w + 8 = -3 $

Subtract 8 from both sides:
$$
w = -3 - 8 = -11
$$
✔ Answer: $ w = -11 $

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#### 2. $ -1 + x = -10 $

Add 1 to both sides:
$$
x = -10 + 1 = -9
$$
✔ Answer: $ x = -9 $

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#### 3. $ 100 = x + 20 $

Subtract 20 from both sides:
$$
x = 100 - 20 = 80
$$
✔ Answer: $ x = 80 $

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#### 4. $ -15 + t = 60 $

Add 15 to both sides:
$$
t = 60 + 15 = 75
$$
✔ Answer: $ t = 75 $

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#### 5. $ x + 12 = 30 $

Subtract 12:
$$
x = 30 - 12 = 18
$$
✔ Answer: $ x = 18 $

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#### 6. $ h + 13 = 7 $

Subtract 13:
$$
h = 7 - 13 = -6
$$
✔ Answer: $ h = -6 $

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#### 7. $ -14 = 3 + x $

Subtract 3:
$$
x = -14 - 3 = -17
$$
✔ Answer: $ x = -17 $

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#### 8. $ 32 = n + 5 $

Subtract 5:
$$
n = 32 - 5 = 27
$$
✔ Answer: $ n = 27 $

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#### 9. $ d - 9 = -5 $

Add 9:
$$
d = -5 + 9 = 4
$$
✔ Answer: $ d = 4 $

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#### 10. $ w - 4 = 8 $

Add 4:
$$
w = 8 + 4 = 12
$$
✔ Answer: $ w = 12 $

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#### 11. $ 28 = h - 11 $

Add 11:
$$
h = 28 + 11 = 39
$$
✔ Answer: $ h = 39 $

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#### 12. $ w - 7 = -20 $

Add 7:
$$
w = -20 + 7 = -13
$$
✔ Answer: $ w = -13 $

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#### 13. $ 12 + n = 7 $

Subtract 12:
$$
n = 7 - 12 = -5
$$
✔ Answer: $ n = -5 $

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#### 14. $ 2 + x = 24 $

Subtract 2:
$$
x = 24 - 2 = 22
$$
✔ Answer: $ x = 22 $

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#### 15. $ -36 = n - 12 $

Add 12:
$$
n = -36 + 12 = -24
$$
✔ Answer: $ n = -24 $

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#### 16. $ 6x = 24 $

Divide by 6:
$$
x = \frac{24}{6} = 4
$$
✔ Answer: $ x = 4 $

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#### 17. $ 9k = 63 $

Divide by 9:
$$
k = \frac{63}{9} = 7
$$
✔ Answer: $ k = 7 $

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#### 18. $ 28 = 2n $

Divide by 2:
$$
n = \frac{28}{2} = 14
$$
✔ Answer: $ n = 14 $

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#### 19. $ -5y = 30 $

Divide by -5:
$$
y = \frac{30}{-5} = -6
$$
✔ Answer: $ y = -6 $

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#### 20. $ -8q = 64 $

Divide by -8:
$$
q = \frac{64}{-8} = -8
$$
✔ Answer: $ q = -8 $

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#### 21. $ -21 = 7m $

Divide by 7:
$$
m = \frac{-21}{7} = -3
$$
✔ Answer: $ m = -3 $

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#### 22. $ 18v = -18 $

Divide by 18:
$$
v = \frac{-18}{18} = -1
$$
✔ Answer: $ v = -1 $

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#### 23. $ -3x = -27 $

Divide by -3:
$$
x = \frac{-27}{-3} = 9
$$
✔ Answer: $ x = 9 $

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#### 24. $ -60 = -12t $

Divide by -12:
$$
t = \frac{-60}{-12} = 5
$$
✔ Answer: $ t = 5 $

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#### 25. $ -x = 11 $

Multiply both sides by -1:
$$
x = -11
$$
✔ Answer: $ x = -11 $

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#### 26. $ \frac{x}{2} = 7 $

Multiply both sides by 2:
$$
x = 7 \times 2 = 14
$$
✔ Answer: $ x = 14 $

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#### 27. $ \frac{n}{7} = 56 $

Multiply by 7:
$$
n = 56 \times 7 = 392
$$
✔ Answer: $ n = 392 $

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#### 28. $ \frac{1}{9}y = 20 $

Multiply by 9:
$$
y = 20 \times 9 = 180
$$
✔ Answer: $ y = 180 $

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#### 29. $ \frac{k}{3} = -4 $

Multiply by 3:
$$
k = -4 \times 3 = -12
$$
✔ Answer: $ k = -12 $

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#### 30. $ 21 = \frac{w}{2} $

Multiply by 2:
$$
w = 21 \times 2 = 42
$$
✔ Answer: $ w = 42 $

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#### 31. $ -3 = \frac{-1}{18}n $

Multiply both sides by 18:
$$
-3 \times 18 = -n \Rightarrow -54 = -n
\Rightarrow n = 54
$$
✔ Answer: $ n = 54 $

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#### 32. $ \frac{1}{2}y = 14 $

Multiply by 2:
$$
y = 14 \times 2 = 28
$$
✔ Answer: $ y = 28 $

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#### 33. $ \frac{6}{5}x = 24 $

Multiply both sides by $ \frac{5}{6} $:
$$
x = 24 \times \frac{5}{6} = 4 \times 5 = 20
$$
✔ Answer: $ x = 20 $

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#### 34. $ \frac{18}{4}v = -18 $

Simplify $ \frac{18}{4} = \frac{9}{2} $
So: $ \frac{9}{2}v = -18 $

Multiply both sides by $ \frac{2}{9} $:
$$
v = -18 \times \frac{2}{9} = -4
$$
✔ Answer: $ v = -4 $

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#### 35. $ \frac{9}{5}k = 63 $

Multiply both sides by $ \frac{5}{9} $:
$$
k = 63 \times \frac{5}{9} = 7 \times 5 = 35
$$
✔ Answer: $ k = 35 $

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#### 36. $ -18 = \frac{x}{4} $

Multiply by 4:
$$
x = -18 \times 4 = -72
$$
✔ Answer: $ x = -72 $

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#### 37. $ \frac{-3}{4}x = -27 $

Multiply both sides by $ \frac{4}{-3} $:
$$
x = -27 \times \frac{4}{-3} = 9 \times 4 = 36
$$
✔ Answer: $ x = 36 $

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#### 38. $ 28 = \frac{2}{3}n $

Multiply both sides by $ \frac{3}{2} $:
$$
n = 28 \times \frac{3}{2} = 14 \times 3 = 42
$$
✔ Answer: $ n = 42 $

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#### 39. $ \frac{-1}{5}x = 11 $

Multiply both sides by -5:
$$
x = 11 \times (-5) = -55
$$
✔ Answer: $ x = -55 $

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#### 40. $ -60 = \frac{-4}{5}t $

Multiply both sides by $ \frac{5}{-4} $:
$$
t = -60 \times \frac{5}{-4} = 60 \times \frac{5}{4} = 15 \times 5 = 75
$$
✔ Answer: $ t = 75 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ w = -11 $ |
| 2 | $ x = -9 $ |
| 3 | $ x = 80 $ |
| 4 | $ t = 75 $ |
| 5 | $ x = 18 $ |
| 6 | $ h = -6 $ |
| 7 | $ x = -17 $ |
| 8 | $ n = 27 $ |
| 9 | $ d = 4 $ |
| 10 | $ w = 12 $ |
| 11 | $ h = 39 $ |
| 12 | $ w = -13 $ |
| 13 | $ n = -5 $ |
| 14 | $ x = 22 $ |
| 15 | $ n = -24 $ |
| 16 | $ x = 4 $ |
| 17 | $ k = 7 $ |
| 18 | $ n = 14 $ |
| 19 | $ y = -6 $ |
| 20 | $ q = -8 $ |
| 21 | $ m = -3 $ |
| 22 | $ v = -1 $ |
| 23 | $ x = 9 $ |
| 24 | $ t = 5 $ |
| 25 | $ x = -11 $ |
| 26 | $ x = 14 $ |
| 27 | $ n = 392 $ |
| 28 | $ y = 180 $ |
| 29 | $ k = -12 $ |
| 30 | $ w = 42 $ |
| 31 | $ n = 54 $ |
| 32 | $ y = 28 $ |
| 33 | $ x = 20 $ |
| 34 | $ v = -4 $ |
| 35 | $ k = 35 $ |
| 36 | $ x = -72 $ |
| 37 | $ x = 36 $ |
| 38 | $ n = 42 $ |
| 39 | $ x = -55 $ |
| 40 | $ t = 75 $ |

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