Solving Basic Equations Worksheets - Free Printable

Let's solve each of these pre-algebra equations step by step using inverse operations. We'll isolate the variable on one side of the equation.

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1. $6 + y \times 1 = 15$

- Simplify: $6 + y = 15$ (since $y \times 1 = y$)
- Subtract 6 from both sides:
$y = 15 - 6$
$y = 9$

✔ Answer: $y = 9$

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2. $12 \times y + y = 52$

- Combine like terms: $12y + y = 13y$
- So: $13y = 52$
- Divide both sides by 13:
$y = \frac{52}{13}$
$y = 4$

✔ Answer: $y = 4$

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3. $8^2 - 7 \times y = 1$

- First, evaluate $8^2 = 64$
- So: $64 - 7y = 1$
- Subtract 64 from both sides:
$-7y = 1 - 64 = -63$
- Divide both sides by -7:
$y = \frac{-63}{-7} = 9$

✔ Answer: $y = 9$

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4. $y^2 - (3 \times 9) = 117$

- First, compute $3 \times 9 = 27$
- So: $y^2 - 27 = 117$
- Add 27 to both sides:
$y^2 = 117 + 27 = 144$
- Take square root of both sides:
$y = \sqrt{144} = 12$ or $y = -12$

⚠️ Since this is a pre-algebra problem and no restriction is given, both solutions are valid unless context implies positive only.

✔ Answer: $y = 12$ or $y = -12$

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5. $y^2 - (7 \times 3) = 79$

- Compute $7 \times 3 = 21$
- So: $y^2 - 21 = 79$
- Add 21 to both sides:
$y^2 = 79 + 21 = 100$
- Take square root:
$y = \sqrt{100} = 10$ or $y = -10$

✔ Answer: $y = 10$ or $y = -10$

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6. $3 \times y - y = 4$

- Combine like terms: $3y - y = 2y$
- So: $2y = 4$
- Divide by 2:
$y = 2$

✔ Answer: $y = 2$

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7. $4 + y \times 9 = 94$

- Rewrite: $4 + 9y = 94$
- Subtract 4 from both sides:
$9y = 90$
- Divide by 9:
$y = 10$

✔ Answer: $y = 10$

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8. $6 \times y + y = 77$

- Combine like terms: $6y + y = 7y$
- So: $7y = 77$
- Divide by 7:
$y = 11$

✔ Answer: $y = 11$

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9. $6 \times y + y = 63$

- Combine like terms: $6y + y = 7y$
- So: $7y = 63$
- Divide by 7:
$y = 9$

✔ Answer: $y = 9$

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10. $1 + 10 \times y = 101$

- Rewrite: $1 + 10y = 101$
- Subtract 1 from both sides:
$10y = 100$
- Divide by 10:
$y = 10$

✔ Answer: $y = 10$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $y = 9$ |
| 2 | $y = 4$ |
| 3 | $y = 9$ |
| 4 | $y = 12$ or $y = -12$ |
| 5 | $y = 10$ or $y = -10$ |
| 6 | $y = 2$ |
| 7 | $y = 10$ |
| 8 | $y = 11$ |
| 9 | $y = 9$ |
| 10 | $y = 10$ |

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Let me know if you'd like these written out with full work shown in a printable format!