Worksheet for solving one-step algebraic equations.

Let's solve each of these one-step algebraic equations step by step. These are simple equations that require only one operation (addition, subtraction, multiplication, or division) to isolate the variable.

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1. $ 12 = \frac{r}{8} $

To solve for $ r $, multiply both sides by 8:

$$
r = 12 \times 8 = 96
$$

✔ Answer: $ r = 96 $

---

2. $ -2 = -4 + p $

Add 4 to both sides:

$$
-2 + 4 = p \Rightarrow p = 2
$$

✔ Answer: $ p = 2 $

---

3. $ \frac{q}{5} = -15 $

Multiply both sides by 5:

$$
q = -15 \times 5 = -75
$$

✔ Answer: $ q = -75 $

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4. $ d - 10 = 8 $

Add 10 to both sides:

$$
d = 8 + 10 = 18
$$

✔ Answer: $ d = 18 $

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5. $ -5 = \frac{a}{18} $

Multiply both sides by 18:

$$
a = -5 \times 18 = -90
$$

✔ Answer: $ a = -90 $

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6. $ -17 = x - 15 $

Add 15 to both sides:

$$
x = -17 + 15 = -2
$$

✔ Answer: $ x = -2 $

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7. $ -10 = \frac{b}{8} $

Multiply both sides by 8:

$$
b = -10 \times 8 = -80
$$

✔ Answer: $ b = -80 $

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8. $ 55 - y = 0 $

Subtract 55 from both sides:

$$
-y = -55
$$

Multiply both sides by -1:

$$
y = 55
$$

✔ Answer: $ y = 55 $

---

9. $ -4 + t = -14 $

Add 4 to both sides:

$$
t = -14 + 4 = -10
$$

✔ Answer: $ t = -10 $

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10. $ -3.5 = \frac{m}{14} $

Multiply both sides by 14:

$$
m = -3.5 \times 14 = -49
$$

✔ Answer: $ m = -49 $

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11. $ k - 4.8 = 7.6 $

Add 4.8 to both sides:

$$
k = 7.6 + 4.8 = 12.4
$$

✔ Answer: $ k = 12.4 $

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12. $ v - \frac{1}{3} = 2\frac{2}{3} $

First, convert the mixed number to an improper fraction:

$$
2\frac{2}{3} = \frac{8}{3}
$$

Now add $ \frac{1}{3} $ to both sides:

$$
v = \frac{8}{3} + \frac{1}{3} = \frac{9}{3} = 3
$$

✔ Answer: $ v = 3 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ r = 96 $ |
| 2 | $ p = 2 $ |
| 3 | $ q = -75 $ |
| 4 | $ d = 18 $ |
| 5 | $ a = -90 $ |
| 6 | $ x = -2 $ |
| 7 | $ b = -80 $ |
| 8 | $ y = 55 $ |
| 9 | $ t = -10 $ |
| 10 | $ m = -49 $ |
| 11 | $ k = 12.4 $ |
| 12 | $ v = 3 $ |

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