https://file.aiquickdraw.com/mathbot/file/1728563123963t53wvobm.jpg

Write a two column proof for the given equation

Let's analyze the two equations given in the image and write a two-column proof for each.

### Problem 3: 
\[
\frac{m}{-3} + 10 = -1
\]
We aim to solve for \( m \). Here is the two-column proof:

| **Step**                      | **Reason**                             |
|-------------------------------|----------------------------------------|
| 1. \( \frac{m}{-3} + 10 = -1 \)    | Given equation                        |
| 2. \( \frac{m}{-3} = -1 - 10 \)    | Subtract 10 from both sides           |
| 3. \( \frac{m}{-3} = -11 \)        | Simplification                        |
| 4. \( m = -11 \times -3 \)         | Multiply both sides by -3             |
| 5. \( m = 33 \)                    | Simplification                        |

### Problem 4: 
\[
3x - 2 = 2(x + 5)
\]
We aim to solve for \( x \). Here is the two-column proof:

| **Step**                      | **Reason**                             |
|-------------------------------|----------------------------------------|
| 1. \( 3x - 2 = 2(x + 5) \)        | Given equation                        |
| 2. \( 3x - 2 = 2x + 10 \)         | Distribute 2 on the right-hand side   |
| 3. \( 3x - 2x = 10 + 2 \)         | Subtract \( 2x \) from both sides     |
| 4. \( x = 12 \)                   | Simplification                        |

Let me know if you have any questions or need further details!

Here are 5 related questions to expand understanding:
1. How do you solve an equation with fractions like in Problem 3?
2. What is the distributive property and how is it used in Problem 4?
3. Can you solve the equation \( \frac{n}{5} + 6 = 2 \)?
4. What happens if there are variables on both sides of the equation?
5. How do you solve multi-step equations in general?

**Tip:** Always isolate the variable by reversing operations in the opposite order of operations (PEMDAS).

Solve the equations: (1) m / -3 + 10 = -1 and (2) 3x - 2 = 2(x + 5)

Learn how to solve linear equations like m / -3 + 10 = -1 and 3x - 2 = 2(x + 5) step by step. This solution explains key algebraic concepts and provides insights into how to use properties of equality and the distributive property. Suitable for students in Grades 6-8.

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