Pre-algebra Worksheet - Free Printable

Problem: Solve for the variable in each equation.

We will solve each equation step by step. Let's go through them one by one.

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#### 1. \( 0 \times y = 0 \)
- Any number multiplied by 0 is 0.
- Therefore, \( y \) can be any real number.
- Solution: \( y = \text{any real number} \)

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#### 2. \( 8 - 1y = 2 \)
- Simplify: \( 8 - y = 2 \)
- Subtract 8 from both sides: \( -y = 2 - 8 \)
- Simplify: \( -y = -6 \)
- Multiply both sides by -1: \( y = 6 \)
- Solution: \( y = 6 \)

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#### 3. \( 63 = y \times 9 \)
- Simplify: \( 63 = 9y \)
- Divide both sides by 9: \( y = \frac{63}{9} \)
- Simplify: \( y = 7 \)
- Solution: \( y = 7 \)

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#### 4. \( 6 - y = 7 \)
- Subtract 6 from both sides: \( -y = 7 - 6 \)
- Simplify: \( -y = 1 \)
- Multiply both sides by -1: \( y = -1 \)
- Solution: \( y = -1 \)

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#### 5. \( 5 - 3y = 2 \)
- Subtract 5 from both sides: \( -3y = 2 - 5 \)
- Simplify: \( -3y = -3 \)
- Divide both sides by -3: \( y = \frac{-3}{-3} \)
- Simplify: \( y = 1 \)
- Solution: \( y = 1 \)

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#### 6. \( 4 = 22 - 6y \)
- Subtract 22 from both sides: \( 4 - 22 = -6y \)
- Simplify: \( -18 = -6y \)
- Divide both sides by -6: \( y = \frac{-18}{-6} \)
- Simplify: \( y = 3 \)
- Solution: \( y = 3 \)

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#### 7. \( 2 = y - (-1) \)
- Simplify: \( 2 = y + 1 \)
- Subtract 1 from both sides: \( y = 2 - 1 \)
- Simplify: \( y = 1 \)
- Solution: \( y = 1 \)

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#### 8. \( 6 = y \times -2 \)
- Simplify: \( 6 = -2y \)
- Divide both sides by -2: \( y = \frac{6}{-2} \)
- Simplify: \( y = -3 \)
- Solution: \( y = -3 \)

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#### 9. \( 0 = 9 - y \)
- Add \( y \) to both sides: \( y = 9 \)
- Solution: \( y = 9 \)

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#### 10. \( 10 = 8 - y \)
- Subtract 8 from both sides: \( 10 - 8 = -y \)
- Simplify: \( 2 = -y \)
- Multiply both sides by -1: \( y = -2 \)
- Solution: \( y = -2 \)

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#### 11. \( 0 = 21 - 7y \)
- Add \( 7y \) to both sides: \( 7y = 21 \)
- Divide both sides by 7: \( y = \frac{21}{7} \)
- Simplify: \( y = 3 \)
- Solution: \( y = 3 \)

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#### 12. \( 2 = 5y - 8 \)
- Add 8 to both sides: \( 2 + 8 = 5y \)
- Simplify: \( 10 = 5y \)
- Divide both sides by 5: \( y = \frac{10}{5} \)
- Simplify: \( y = 2 \)
- Solution: \( y = 2 \)

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#### 13. \( y - 1 = 8 \)
- Add 1 to both sides: \( y = 8 + 1 \)
- Simplify: \( y = 9 \)
- Solution: \( y = 9 \)

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#### 14. \( y - 4 = 3 \)
- Add 4 to both sides: \( y = 3 + 4 \)
- Simplify: \( y = 7 \)
- Solution: \( y = 7 \)

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#### 15. \( 4 = y - 5 \)
- Add 5 to both sides: \( 4 + 5 = y \)
- Simplify: \( y = 9 \)
- Solution: \( y = 9 \)

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#### 16. \( 5y - 6 = 4 \)
- Add 6 to both sides: \( 5y = 4 + 6 \)
- Simplify: \( 5y = 10 \)
- Divide both sides by 5: \( y = \frac{10}{5} \)
- Simplify: \( y = 2 \)
- Solution: \( y = 2 \)

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#### 17. \( 1y - 1 = 5 \)
- Simplify: \( y - 1 = 5 \)
- Add 1 to both sides: \( y = 5 + 1 \)
- Simplify: \( y = 6 \)
- Solution: \( y = 6 \)

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#### 18. \( 2y - 5 = 3 \)
- Add 5 to both sides: \( 2y = 3 + 5 \)
- Simplify: \( 2y = 8 \)
- Divide both sides by 2: \( y = \frac{8}{2} \)
- Simplify: \( y = 4 \)
- Solution: \( y = 4 \)

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#### 19. \( 12 = y \times 6 \)
- Simplify: \( 12 = 6y \)
- Divide both sides by 6: \( y = \frac{12}{6} \)
- Simplify: \( y = 2 \)
- Solution: \( y = 2 \)

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#### 20. \( 9 = 9 - 3y \)
- Subtract 9 from both sides: \( 0 = -3y \)
- Divide both sides by -3: \( y = \frac{0}{-3} \)
- Simplify: \( y = 0 \)
- Solution: \( y = 0 \)

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#### 21. \( 1 = 1y - 2 \)
- Simplify: \( 1 = y - 2 \)
- Add 2 to both sides: \( y = 1 + 2 \)
- Simplify: \( y = 3 \)
- Solution: \( y = 3 \)

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#### 22. \( 8 - y = 6 \)
- Subtract 8 from both sides: \( -y = 6 - 8 \)
- Simplify: \( -y = -2 \)
- Multiply both sides by -1: \( y = 2 \)
- Solution: \( y = 2 \)

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#### 23. \( 3 = 8 - y \)
- Subtract 8 from both sides: \( 3 - 8 = -y \)
- Simplify: \( -5 = -y \)
- Multiply both sides by -1: \( y = 5 \)
- Solution: \( y = 5 \)

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#### 24. \( y \times 9 = 27 \)
- Simplify: \( 9y = 27 \)
- Divide both sides by 9: \( y = \frac{27}{9} \)
- Simplify: \( y = 3 \)
- Solution: \( y = 3 \)

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#### 25. \( y \times 0 = 0 \)
- Any number multiplied by 0 is 0.
- Therefore, \( y \) can be any real number.
- Solution: \( y = \text{any real number} \)

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#### 26. \( 6 = 9 - y \)
- Subtract 9 from both sides: \( 6 - 9 = -y \)
- Simplify: \( -3 = -y \)
- Multiply both sides by -1: \( y = 3 \)
- Solution: \( y = 3 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \text{any real number} \\
2. & 6 \\
3. & 7 \\
4. & -1 \\
5. & 1 \\
6. & 3 \\
7. & 1 \\
8. & -3 \\
9. & 9 \\
10. & -2 \\
11. & 3 \\
12. & 2 \\
13. & 9 \\
14. & 7 \\
15. & 9 \\
16. & 2 \\
17. & 6 \\
18. & 4 \\
19. & 2 \\
20. & 0 \\
21. & 3 \\
22. & 2 \\
23. & 5 \\
24. & 3 \\
25. & \text{any real number} \\
26. & 3 \\
\end{array}
}
\]