Question

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

Answer 1

What is the property for reason 1?

Answer 2

To prove that \( x = -1 \) given the equation \(-2(x - 4) = 2x + 12\), we can follow a series of algebraic steps using properties of equations. Here are the statements and their corresponding properties:

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

2. **Statement 2:** \(-2x + 8 = 2x + 12\)
**Property:** Distributive property (distributing \(-2\) to both \(x\) and \(-4\))

3. **Statement 3:** \(-2x - 2x + 8 = 12\)
**Property:** Addition of \(2x\) to both sides

4. **Statement 4:** \(-4x + 8 = 12\)
**Property:** Combine like terms (collecting \(x\) terms)

5. **Statement 5:** \(-4x = 12 - 8\)
**Property:** Subtraction of \(8\) from both sides

6. **Statement 6:** \(-4x = 4\)
**Property:** Simplification

7. **Statement 7:** \(x = \frac{4}{-4}\)
**Property:** Division by \(-4\)

8. **Statement 8:** \(x = -1\)
**Property:** Simplification

Thus, we have proven \( x = -1 \) through a sequence of logical statements and properties.

Answer 3

For **Statement 1**: \(-2(x - 4) = 2x + 12\), the reason or property is simply:

**Property:** Given

This indicates that this equation is the starting point of the proof, and it is the equation we are working with to show that \(x = -1\).