Let's go over the equations shown in your homework. I’ll provide detailed steps for solving each one. These problems involve solving linear equations with variables on both sides.

1) $-x + 7 = 5x + 7 - 6x$

• Combine like terms on the right side: $5x - 6x = -x$
• The equation becomes $-x + 7 = -x + 7$
• Subtract $-x$ from both sides: $7 = 7$
• This equation is an identity, meaning it's true for all values of $x$.

2) $8 + x - 6 + 3 = x + 5$

• Simplify the left side: $8 - 6 + 3 = 5$, so the equation becomes $5 + x = x + 5$
• Subtract $x$ from both sides: $5 = 5$
• This is also an identity, so it's true for all $x$.

3) $-9 - x = -x - 5$

• Add $x$ to both sides: $-9 = -5$
• This is a contradiction (since $-9$ is not equal to $-5$), meaning there is no solution.

4) $1 + 3v = 11 - 6 + 4v - 7$

• Simplify both sides: $1 + 3v = -2 + 4v$
• Subtract $3v$ from both sides: $1 = -2 + v$
• Add 2 to both sides: $3 = v$
• So, $v = 3$.

5) $6 - 5x = 1 - 4x$

• Add $5x$ to both sides: $6 = 1 + x$
• Subtract 1 from both sides: $5 = x$
• So, $x = 5$.

6) $3v - 2 = -4 + 3v$

• Subtract $3v$ from both sides: $-2 = -4$
• This is a contradiction, so there is no solution.

7) $16 - 3 + 7x - 3x = 6x - 1$

• Simplify both sides: $13 + 4x = 6x - 1$
• Subtract $4x$ from both sides: $13 = 2x - 1$
• Add 1 to both sides: $14 = 2x$
• Divide by 2: $x = 7$.

8) $-6n + 7n = -12 - 4n + 2n$

• Combine like terms: $n = -12 - 2n$
• Add $2n$ to both sides: $3n = -12$
• Divide by 3: $n = -4$.

9) $r + 3 + 4 + 11 = -r - 4r$

• Simplify both sides: $r + 18 = -5r$
• Add $5r$ to both sides: $6r + 18 = 0$
• Subtract 18 from both sides: $6r = -18$
• Divide by 6: $r = -3$.

10) $-9 + 8n = 4n + 3$

• Subtract $4n$ from both sides: $-9 + 4n = 3$
• Add 9 to both sides: $4n = 12$
• Divide by 4: $n = 3$.

Would you like further details or explanations for any of these solutions?

Here are 5 related questions to practice:

1. Solve: $2x + 3 = 7x - 9$
2. Solve: $4 - 2n = 3n + 5$
3. Solve: $5x - 7 = 3x + 9 - 4x$
4. Solve: $6y + 2 - 3y = y - 4$
5. Solve: $8z + 3 = 4z + 19$

Tip: Always combine like terms on each side of the equation before moving variables or constants across the equal sign.