Linear Equations Worksheet for solving algebraic equations.

1. $x + 6 = 9$
- Subtract 6 from both sides: $x = 9 - 6$
- $x = 3$

2. $3(x - 2) = 6$
- Distribute 3: $3x - 6 = 6$
- Add 6 to both sides: $3x = 12$
- Divide by 3: $x = 4$

3. $10 - x = 6$
- Subtract 10 from both sides: $-x = -4$
- Multiply by -1: $x = 4$

4. $-y = -12$
- Multiply by -1: $y = 12$

5. $6 - \frac{x}{4} = -\frac{x}{4}$
- Add $\frac{x}{4}$ to both sides: $6 = 0$
- This is a contradiction, so no solution.

6. $-5x = -7 + 2x$
- Subtract 2x from both sides: $-7x = -7$
- Divide by -7: $x = 1$

7. $n - 4n = 14 - 3n$
- Simplify: $-3n = 14 - 3n$
- Add 3n to both sides: $0 = 14$
- This is a contradiction, so no solution.

8. $\frac{1}{7}x = 2$
- Multiply both sides by 7: $x = 14$

9. $4x = -32$
- Divide by 4: $x = -8$

10. $4 = -2(x + 3)$
- Distribute -2: $4 = -2x - 6$
- Add 6 to both sides: $10 = -2x$
- Divide by -2: $x = -5$

11. $\frac{x}{3} = -9$
- Multiply both sides by 3: $x = -27$

12. $-\frac{9}{6}x = -40$
- Simplify: $-\frac{3}{2}x = -40$
- Multiply both sides by $-\frac{2}{3}$: $x = \frac{80}{3}$

13. $-2x - 6x = 1$
- Combine like terms: $-8x = 1$
- Divide by -8: $x = -\frac{1}{8}$

14. $10x - x = -9$
- Combine like terms: $9x = -9$
- Divide by 9: $x = -1$