https://file.aiquickdraw.com/mathbot/file/1726112840896y4k86m1n.jpg

Let's go over the two-step equations in the image one by one. I'll solve them step-by-step.

1. **\( 5n + 5 = 100 \)**  
   **Solution:**  
   Subtract 5 from both sides:  
   \[
   5n = 100 - 5
   \]
   \[
   5n = 95
   \]
   Divide both sides by 5:  
   \[
   n = \frac{95}{5} = 19
   \]

2. **\( \frac{n - 9}{9} = 2 \)**  
   **Solution:**  
   Multiply both sides by 9:  
   \[
   n - 9 = 18
   \]
   Add 9 to both sides:  
   \[
   n = 18 + 9 = 27
   \]

3. **\( \frac{n}{6} + 2 = 2 \)**  
   **Solution:**  
   Subtract 2 from both sides:  
   \[
   \frac{n}{6} = 0
   \]
   Multiply both sides by 6:  
   \[
   n = 0
   \]

4. **\( \frac{x}{6} + 4 = 7 \)**  
   **Solution:**  
   Subtract 4 from both sides:  
   \[
   \frac{x}{6} = 3
   \]
   Multiply both sides by 6:  
   \[
   x = 18
   \]

5. **\( 10 - 10 = 8n \)** (This one seems to be a bit unclear. Can you confirm if there's a typo here?)

6. **\( -58 = -8a - 2 \)**  
   **Solution:**  
   Add 2 to both sides:  
   \[
   -58 + 2 = -8a
   \]
   \[
   -56 = -8a
   \]
   Divide both sides by -8:  
   \[
   a = \frac{-56}{-8} = 7
   \]

7. **\( \frac{8 + x}{3} = 7 \)**  
   **Solution:**  
   Multiply both sides by 3:  
   \[
   8 + x = 21
   \]
   Subtract 8 from both sides:  
   \[
   x = 21 - 8 = 13
   \]

8. **\( -6x + 7 = 37 \)**  
   **Solution:**  
   Subtract 7 from both sides:  
   \[
   -6x = 30
   \]
   Divide both sides by -6:  
   \[
   x = \frac{30}{-6} = -5
   \]

9. **\( -x - 10 = -15 \)**  
   **Solution:**  
   Add 10 to both sides:  
   \[
   -x = -15 + 10
   \]
   \[
   -x = -5
   \]
   Multiply both sides by -1:  
   \[
   x = 5
   \]

Would you like a more detailed explanation for any of these problems, or help with any other steps?

### 5 Related Questions:
1. How do you handle equations with variables on both sides?
2. What happens if there are parentheses in the equation?
3. How would you solve an equation with fractions on both sides?
4. How do you check if a solution to an equation is correct?
5. What are the different methods for solving quadratic equations?

### Tip:
Always check your answer by substituting the solution back into the original equation to verify it's correct.

Solve two-step equations from an image containing algebra problems.

Detailed solutions to two-step algebraic equations, including subtraction, division, and handling variables on both sides of the equation. Suitable for students in Grades 7-8.

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