Pre-Algebra Equations worksheet for solving unknown variables using inverse operations.

Let's solve each of these pre-algebra equations step by step using inverse operations. The goal is to isolate the variable $ y $ on one side of the equation.

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1. $ \frac{y}{1} + 6 = 11 $

- $ \frac{y}{1} $ is just $ y $
- So: $ y + 6 = 11 $
- Subtract 6 from both sides:
$$
y = 11 - 6 = 5
$$
✔ Answer: $ y = 5 $

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2. $ 5 + \frac{y}{9} = 6 $

- Subtract 5 from both sides:
$$
\frac{y}{9} = 6 - 5 = 1
$$
- Multiply both sides by 9:
$$
y = 1 \times 9 = 9
$$
✔ Answer: $ y = 9 $

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3. $ \frac{y}{11} + 6 = 7 $

- Subtract 6 from both sides:
$$
\frac{y}{11} = 7 - 6 = 1
$$
- Multiply both sides by 11:
$$
y = 1 \times 11 = 11
$$
✔ Answer: $ y = 11 $

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4. $ 8 + \frac{y}{5} = 8.8 $

- Subtract 8 from both sides:
$$
\frac{y}{5} = 8.8 - 8 = 0.8
$$
- Multiply both sides by 5:
$$
y = 0.8 \times 5 = 4
$$
✔ Answer: $ y = 4 $

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5. $ \frac{y}{4} + 4 = 5.3 $

- Subtract 4 from both sides:
$$
\frac{y}{4} = 5.3 - 4 = 1.3
$$
- Multiply both sides by 4:
$$
y = 1.3 \times 4 = 5.2
$$
✔ Answer: $ y = 5.2 $

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6. $ \frac{y}{12} + 1 = 1.6 $

- Subtract 1 from both sides:
$$
\frac{y}{12} = 1.6 - 1 = 0.6
$$
- Multiply both sides by 12:
$$
y = 0.6 \times 12 = 7.2
$$
✔ Answer: $ y = 7.2 $

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7. $ \frac{y}{12} + 3 = 3.3 $

- Subtract 3 from both sides:
$$
\frac{y}{12} = 3.3 - 3 = 0.3
$$
- Multiply both sides by 12:
$$
y = 0.3 \times 12 = 3.6
$$
✔ Answer: $ y = 3.6 $

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8. $ \frac{y}{3} + 10 = 13 $

- Subtract 10 from both sides:
$$
\frac{y}{3} = 13 - 10 = 3
$$
- Multiply both sides by 3:
$$
y = 3 \times 3 = 9
$$
✔ Answer: $ y = 9 $

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9. $ \frac{y}{10} + 2 = 2.5 $

- Subtract 2 from both sides:
$$
\frac{y}{10} = 2.5 - 2 = 0.5
$$
- Multiply both sides by 10:
$$
y = 0.5 \times 10 = 5
$$
✔ Answer: $ y = 5 $

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10. $ \frac{y}{12} + 1 = 1.3 $

- Subtract 1 from both sides:
$$
\frac{y}{12} = 1.3 - 1 = 0.3
$$
- Multiply both sides by 12:
$$
y = 0.3 \times 12 = 3.6
$$
✔ Answer: $ y = 3.6 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ y = 5 $ |
| 2 | $ y = 9 $ |
| 3 | $ y = 11 $ |
| 4 | $ y = 4 $ |
| 5 | $ y = 5.2 $ |
| 6 | $ y = 7.2 $ |
| 7 | $ y = 3.6 $ |
| 8 | $ y = 9 $ |
| 9 | $ y = 5 $ |
| 10 | $ y = 3.6 $ |

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🔍 Summary of Strategy:

For each equation:
1. Isolate the term with $ y $ by subtracting constants.
2. Eliminate the denominator by multiplying both sides by the denominator.
3. Simplify to find $ y $.

This method uses inverse operations: subtraction to undo addition, multiplication to undo division.

Let me know if you'd like a printed version or explanation for any specific problem!