The problem is to solve the following five linear equations: 1. $8 - 8x = 9 - 9x$

1. Problem Description

The problem is to solve the following five linear equations:

1. $8 - 8x = 9 - 9x$

2. $2 - q = q - 4$

3. $2x + 5 = 3x - 7$

4. $13x - 12 = 5x + 60$

5. $3 + 3y = 1 - 13y$

2. Solution Steps

1. $8 - 8x = 9 - 9x$

Add $9x$ to both sides: $8 - 8x + 9x = 9 - 9x + 9x$ which simplifies to $8 + x = 9$.

Subtract 8 from both sides: $8 + x - 8 = 9 - 8$ which simplifies to $x = 1$.

2. $2 - q = q - 4$

Add $q$ to both sides: $2 - q + q = q - 4 + q$ which simplifies to $2 = 2q - 4$.

Add 4 to both sides: $2 + 4 = 2q - 4 + 4$ which simplifies to $6 = 2q$.

Divide both sides by 2: $\frac{6}{2} = \frac{2q}{2}$ which simplifies to $q = 3$.

3. $2x + 5 = 3x - 7$

Subtract $2x$ from both sides: $2x + 5 - 2x = 3x - 7 - 2x$ which simplifies to $5 = x - 7$.

Add 7 to both sides: $5 + 7 = x - 7 + 7$ which simplifies to $12 = x$. Therefore, $x = 12$.

4. $13x - 12 = 5x + 60$

Subtract $5x$ from both sides: $13x - 12 - 5x = 5x + 60 - 5x$ which simplifies to $8x - 12 = 60$.

Add 12 to both sides: $8x - 12 + 12 = 60 + 12$ which simplifies to $8x = 72$.

Divide both sides by 8: $\frac{8x}{8} = \frac{72}{8}$ which simplifies to $x = 9$.

5. $3 + 3y = 1 - 13y$

Add $13y$ to both sides: $3 + 3y + 13y = 1 - 13y + 13y$ which simplifies to $3 + 16y = 1$.

Subtract 3 from both sides: $3 + 16y - 3 = 1 - 3$ which simplifies to $16y = -2$.

Divide both sides by 16: $\frac{16y}{16} = \frac{-2}{16}$ which simplifies to $y = -\frac{1}{8}$.

3. Final Answer

1. $x = 1$

2. $q = 3$

3. $x = 12$

4. $x = 9$

5. $y = -\frac{1}{8}$