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Let's break down the two-column proof for the equation \(3x + 1 = -14\) step by step.

### Given:
\[
3x + 1 = -14
\]

### Steps:

1. **Start with the given equation:**
   - **Statement:** \(3x + 1 = -14\)
   - **Reason:** Given

2. **Subtract 1 from both sides:**
   - **Statement:** \(3x = -15\)
   - **Reason:** Subtraction Property of Equality

3. **Divide both sides by 3:**
   - **Statement:** \(x = -5\)
   - **Reason:** Division Property of Equality

Now, the blank in the "Reason" column in step 2 is filled with the **Subtraction Property of Equality**.

Would you like more details, or do you have any questions?

Here are five related questions for deeper understanding:
1. What is the purpose of a two-column proof in algebra?
2. How does the Subtraction Property of Equality work?
3. Could we rearrange the steps in a different order while solving this equation?
4. How does solving equations with variables on both sides differ from this example?
5. What are some real-life applications of solving linear equations?

**Tip:** Always check your solution by substituting the value of \(x\) back into the original equation to verify your answer.

Fill in the blank for the following two-column proof: Given: 3x + 1 = -14, Prove: x = -5.

Learn how to solve the linear equation 3x + 1 = -14 using a two-column proof. This solution demonstrates key algebraic properties, including the Subtraction and Division Properties of Equality. Suitable for students in Grades 7-8.

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