Question

Given: -2(x - 4) = 2x + 12 Prove: x = -1
Statements and Reasons
Statement 1: -2(x - 4) = 2x + 12. Reasons: _____

Answer 1

Let's break down the steps and provide the necessary statements and reasons for solving the equation \(-2(x - 4) = 2x + 12\) to prove that \(x = -1\).

### Proof Steps

1. **Statement 1:**
\[-2(x - 4) = 2x + 12\]
**Reason:** Given.

2. **Statement 2:**
\[-2x + 8 = 2x + 12\]
**Reason:** Distribute \(-2\) on the left side.

3. **Statement 3:**
\[-2x + 8 - 12 = 2x + 12 - 12\]
**Reason:** Subtract \(12\) from both sides.

4. **Statement 4:**
\[-2x - 4 = 2x\]
**Reason:** Simplify left side.

5. **Statement 5:**
\[-2x - 4 - 2x = 2x - 2x\]
**Reason:** Subtract \(2x\) from both sides.

6. **Statement 6:**
\[-4 - 4x = 0\]
**Reason:** Combine like terms on the left side.

7. **Statement 7:**
\[-4x = 4\]
**Reason:** Add \(4\) to both sides.

8. **Statement 8:**
\(x = \frac{4}{-4}\)
**Reason:** Divide both sides by \(-4\).

9. **Statement 9:**
\(x = -1\)
**Reason:** Simplify \(\frac{4}{-4}\).

### Conclusion
Thus, we have shown that \(x = -1\) through algebraic manipulation of the given equation.