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Solving Linear Equations (C)

1. $x + 10 = 30$
2. $x - 8 = 20$
3. $2x = 65$
4. $9 + 4x = -15$
5. $14 + 6x = 2$
6. $2x - 3 = -2$
7. $5 + 10x = -15$
8. $10 - 7x$
9. $-3 = 16 - x$
10. $-4 = 12 - 2x$
11. $25 = 46 - 3x$
12. $8 = 9 - 5x$
13. $11 = 19$
14. $3 = \frac{x}{4}$
15. $7 = \frac{x}{2} - 4$
16. $-2 = \frac{x}{8} - 5$
17. $-1 = 6 + \frac{x}{2}$
18. $14 - \frac{x}{3} = 10$
19. $5 - \frac{x}{9} = -1$
20. $\frac{x+5}{3} = 12$
21. $\frac{x-4}{11} = 9$
22. $\frac{x+3}{8} = -2$

Here are the solutions to the linear equations:

1. $x + 10 = 30$ $x = 30 - 10$ $x = 20$

2. $x - 8 = 20$ $x = 20 + 8$ $x = 28$

3. $2x = 65$ $x = \frac{65}{2}$ $x = 32.5$

4. $9 + 4x = -15$ $4x = -15 - 9$ $4x = -24$ $x = \frac{-24}{4}$ $x = -6$

5. $14 + 6x = 2$ $6x = 2 - 14$ $6x = -12$ $x = \frac{-12}{6}$ $x = -2$

6. $2x - 3 = -2$ $2x = -2 + 3$ $2x = 1$ $x = \frac{1}{2}$

7. $5 + 10x = -15$ $10x = -15 - 5$ $10x = -20$ $x = \frac{-20}{10}$ $x = -2$

8. $10 - 7x$ This is an expression, not an equation. It cannot be solved for $x$ as there is no equality sign.

9. $-3 = 16 - x$ $-3 - 16 = -x$ $-19 = -x$ $x = 19$

10. $-4 = 12 - 2x$ $-4 - 12 = -2x$ $-16 = -2x$ $x = \frac{-16}{-2}$ $x = 8$

11. $25 = 46 - 3x$ $25 - 46 = -3x$ $-21 = -3x$ $x = \frac{-21}{-3}$ $x = 7$

12. $8 = 9 - 5x$ $8 - 9 = -5x$ $-1 = -5x$ $x = \frac{-1}{-5}$ $x = \frac{1}{5}$

13. $11 = 19$ This is a false statement, not an equation to solve for $x$. There is no variable $x$ present.

14. $3 = \frac{x}{4}$ $3 \times 4 = x$ $x = 12$

15. $7 = \frac{x}{2} - 4$ $7 + 4 = \frac{x}{2}$ $11 = \frac{x}{2}$ $11 \times 2 = x$ $x = 22$

16. $-2 = \frac{x}{8} - 5$ $-2 + 5 = \frac{x}{8}$ $3 = \frac{x}{8}$ $3 \times 8 = x$ $x = 24$

17. $-1 = 6 + \frac{x}{2}$ $-1 - 6 = \frac{x}{2}$ $-7 = \frac{x}{2}$ $-7 \times 2 = x$ $x = -14$

18. $14 - \frac{x}{3} = 10$ $-\frac{x}{3} = 10 - 14$ $-\frac{x}{3} = -4$ $x = -4 \times (-3)$ $x = 12$

19. $5 - \frac{x}{9} = -1$ $-\frac{x}{9} = -1 - 5$ $-\frac{x}{9} = -6$ $x = -6 \times (-9)$ $x = 54$

20. $\frac{x+5}{3} = 12$ $x+5 = 12 \times 3$ $x+5 = 36$ $x = 36 - 5$ $x = 31$

21. $\frac{x-4}{11} = 9$ $x-4 = 9 \times 11$ $x-4 = 99$ $x = 99 + 4$ $x = 103$

22. $\frac{x+3}{8} = -2$ $x+3 = -2 \times 8$ $x+3 = -16$ $x = -16 - 3$ $x = -19$