To write a two-column proof for solving the equation \( 25 + 5(4 - x) = 5 \), we will display each step of the solution along with its justification in two columns: one for the steps and one for the reasons (justifications).

### Two-Column Proof for \( 25 + 5(4 - x) = 5 \)

| **Steps**                                    | **Reasons**                                            |
|----------------------------------------------|-------------------------------------------------------|
| 1. \( 25 + 5(4 - x) = 5 \)                   | Given                                                 |
| 2. \( 25 + 20 - 5x = 5 \)                    | Distribute \( 5 \) over \( (4 - x) \)                 |
| 3. \( 45 - 5x = 5 \)                        | Simplify \( 25 + 20 \) to \( 45 \)                    |
| 4. \( -5x = 5 - 45 \)                       | Subtract 45 from both sides                           |
| 5. \( -5x = -40 \)                          | Simplify \( 5 - 45 \)                                 |
| 6. \( x = \frac{-40}{-5} \)                 | Divide both sides by \(-5\)                           |
| 7. \( x = 8 \)                              | Simplify \( \frac{-40}{-5} \)                         |

### Final Answer: \( x = 8 \)

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Would you like more details on any of the steps? 

Here are 5 related questions to expand your understanding:

1. How do you know when to distribute in an equation like this?
2. Can you apply similar steps to solve \( 30 + 2(5 - x) = 8 \)?
3. How would the solution change if the equation was \( 25 + 5(x - 4) = 5 \)?
4. Why is dividing both sides by a negative number important when isolating \( x \)?
5. How would you check the solution once you have found \( x \)?

**Tip**: Always simplify the terms inside parentheses before applying operations to make the solving process clearer.

Explore how to solve the linear equation 25 + 5(4 - x) = 5 using a detailed two-column proof. This step-by-step solution demonstrates key algebraic concepts, including the distributive property and solving for a variable. Ideal for students in Grades 7-9.

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