Given: -2(x - 4) = 2x + 12 Prove: x = -1

Question

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

Answer 1

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 2

What is the property for reason 1?

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 \(x = -1\).