To solve the equation \( 2x + 3 + 5x = -18 \) using a **two-column proof**, we can format it as follows:

| **Steps** (Statements)               | **Reasons** (Justifications)                        |
|--------------------------------------|----------------------------------------------------|
| 1. \( 2x + 3 + 5x = -18 \)           | Given Equation                                     |
| 2. \( 7x + 3 = -18 \)                | Combine like terms \( 2x + 5x = 7x \)              |
| 3. \( 7x = -18 - 3 \)                | Subtract 3 from both sides                         |
| 4. \( 7x = -21 \)                    | Simplify \( -18 - 3 = -21 \)                       |
| 5. \( x = \frac{-21}{7} \)           | Divide both sides by 7                             |
| 6. \( x = -3 \)                      | Simplify \( \frac{-21}{7} = -3 \)                  |

### Solution:
The solution to the equation is \( x = -3 \).

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### 5 Related Questions:
1. How would you check if \( x = -3 \) is correct in the original equation?
2. What are some other methods to solve this equation?
3. How do we apply a two-column proof in geometry compared to algebra?
4. What happens if there were no solution or infinitely many solutions?
5. How would this change if the equation involved fractions or decimals?

### Tip:
When solving algebraic equations, always check your solution by substituting it back into the original equation to verify its accuracy.

Explore a step-by-step solution to the linear equation 2x + 3 + 5x = -18 using a two-column proof format. Learn how to combine like terms, subtract constants, and isolate the variable. Suitable for students in Grades 6-8.

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