Math worksheet for solving linear equations with various algebraic expressions and variables.

Since both `ExplainAnswer` and `TeachTopic` are false, I will proceed directly to solving the problems and providing the final answers.

Here are the step-by-step solutions for each equation on the worksheet:

1. Solve for m:
Equation: $2(m + 6) = 48$
- Divide both sides by 2: $m + 6 = 24$
- Subtract 6 from both sides: $m = 18$

2. Solve for x:
Equation: $8x + 9 - 3x = 8 + 4x + 5$
- Combine like terms on the left side ($8x - 3x$): $5x + 9 = 8 + 4x + 5$
- Combine like terms on the right side ($8 + 5$): $5x + 9 = 13 + 4x$
- Subtract $4x$ from both sides: $x + 9 = 13$
- Subtract 9 from both sides: $x = 4$

3. Solve for a:
Equation: $8a - (4a + 32) = 16$
- Distribute the negative sign: $8a - 4a - 32 = 16$
- Combine like terms ($8a - 4a$): $4a - 32 = 16$
- Add 32 to both sides: $4a = 48$
- Divide by 4: $a = 12$

4. Solve for x:
Equation: $-3(x - 1) + 8(x - 3) = 6x + 7 - 5x$
- Distribute on the left side: $-3x + 3 + 8x - 24 = 6x + 7 - 5x$
- Combine like terms on the left ($-3x + 8x$ and $3 - 24$): $5x - 21 = 6x + 7 - 5x$
- Combine like terms on the right ($6x - 5x$): $5x - 21 = x + 7$
- Subtract $x$ from both sides: $4x - 21 = 7$
- Add 21 to both sides: $4x = 28$
- Divide by 4: $x = 7$

5. Solve for x:
Equation: $10x + 5(5x - 3) = 5(6x + 4)$
- Distribute on both sides: $10x + 25x - 15 = 30x + 20$
- Combine like terms on the left: $35x - 15 = 30x + 20$
- Subtract $30x$ from both sides: $5x - 15 = 20$
- Add 15 to both sides: $5x = 35$
- Divide by 5: $x = 7$

6. Solve for m:
Equation: $0.02m + 0.08(8 - m) = 1.78$
- Distribute the 0.08: $0.02m + 0.64 - 0.08m = 1.78$
- Combine like terms ($0.02m - 0.08m$): $-0.06m + 0.64 = 1.78$
- Subtract 0.64 from both sides: $-0.06m = 1.14$
- Divide by -0.06: $m = -19$

7. Solve for x:
Equation: $\frac{1}{3}(10 - 2x) = \frac{1}{3}(8 - 2x)$
- Since both sides are multiplied by $\frac{1}{3}$, we can multiply the entire equation by 3 to clear the fractions: $10 - 2x = 8 - 2x$
- Add $2x$ to both sides: $10 = 8$
- This is a false statement ($10$ does not equal $8$). Therefore, there is no solution.

8. Solve for b:
Equation: $-14 + 6b + 7 - 2b = 1 + 5b$
- Combine like terms on the left ($6b - 2b$ and $-14 + 7$): $4b - 7 = 1 + 5b$
- Subtract $4b$ from both sides: $-7 = 1 + b$
- Subtract 1 from both sides: $-8 = b$

Final Answer:
1. m = 18
2. x = 4
3. a = 12
4. x = 7
5. x = 7
6. m = -19
7. No solution
8. b = -8