https://file.aiquickdraw.com/mathbot/file/1726113389598vuhwvakg.jpg

Let's go through these multi-step equations one by one.

1. **\( 6a + 5a = -11 \)**
   - Combine like terms: \( 6a + 5a = 11a \)
   - Now solve: \( 11a = -11 \)
   - Divide both sides by 11: \( a = -1 \)

2. **\( -6a - 2n = 16 \)**
   - We can't combine terms, but solve for \( n \):
   - Isolate \( -2n \) by adding \( 6a \) to both sides:
     \( -2n = 16 + 6a \)

3. **\( 4x + 6 + 3 = 17 \)**
   - Combine like terms: \( 4x + 9 = 17 \)
   - Subtract 9 from both sides: \( 4x = 8 \)
   - Divide by 4: \( x = 2 \)

4. **\( 0 = -5n - 2n \)**
   - Combine like terms: \( 0 = -7n \)
   - Divide by -7: \( n = 0 \)

5. **\( 6r - 1 + 6r = 11 \)**
   - Combine like terms: \( 12r - 1 = 11 \)
   - Add 1 to both sides: \( 12r = 12 \)
   - Divide by 12: \( r = 1 \)

6. **\( r + 11 + 8r = 29 \)**
   - Combine like terms: \( 9r + 11 = 29 \)
   - Subtract 11 from both sides: \( 9r = 18 \)
   - Divide by 9: \( r = 2 \)

7. **\( -10 = -14v + 14v \)**
   - \( -14v + 14v = 0 \), so the equation simplifies to \( -10 = 0 \), which is a contradiction. This means there is no solution.

8. **\( -10p + 9p = 12 \)**
   - Combine like terms: \( -p = 12 \)
   - Multiply by -1: \( p = -12 \)

9. **\( 42 = 8m + 13m \)**
   - Combine like terms: \( 42 = 21m \)
   - Divide by 21: \( m = 2 \)

Let me know if you need further explanations or details on any of the steps! 

### 5 related questions:
1. How do you solve equations with variables on both sides?
2. How do you handle equations with no solutions or infinite solutions?
3. How can you verify your solutions to an equation?
4. What happens when you get a contradiction like in problem 7?
5. How do you combine like terms in more complex equations?

### Tip:
Always simplify equations by combining like terms and isolating the variable to make solving easier.

Homework 7: Multi-Step Equations. Solve the following multi-step equations.

Learn how to solve multi-step algebraic equations involving combining like terms. This guide includes step-by-step solutions for problems like 6a + 5a = -11 and 42 = 8m + 13m, suitable for Grades 7-8.

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