Question

Type your answer in the boxes for the correct statement or reasons for the following proof.
Pro-tip: Solve the problem first
Given -2(x-4)=2x+12 Prove:x=-1
Statements: Reason:
1S. -2(x-4)=2x+12 1R._________________
2S. ________________ 2R. Distributive Property
3S. __________________ 3R.__________________
4S. -x-4=4 4R.__________________
5S.____________________ 5R.Divisions property of equality

Answer 1

there is 5 of them, you didn't provide number three correctly

Answer 2

To prove that \( x = -1 \) given the equation \( -2(x - 4) = 2x + 12 \), we will solve the equation step by step.

1. **Start with the Given Equation:**
\[
-2(x - 4) = 2x + 12
\]

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

2. **Apply the Distributive Property to the left side:**
\[
-2x + 8 = 2x + 12
\]

**Statement 2:**
\[
-2x + 8 = 2x + 12
\]
**Reason 2:**
\[
Distributive Property
\]

3. **Move all terms involving \( x \) to one side and constants to the other side:**
\[
-2x - 2x = 12 - 8
\]
This simplifies to:
\[
-4x = 4
\]

**Statement 3:**
\[
-4x = 4
\]
**Reason 3:**
\[
Addition Property of Equality
\]

4. **Divide both sides by -4:**
\[
x = -1
\]

**Statement 4:**
\[
x = -1
\]
**Reason 4:**
\[
Division Property of Equality
\]

Now we can fill in the missing parts of your proof:

- Reason for Statement 1: **Given**
- Statement 2: **\(-2x + 8 = 2x + 12\)**
- Reason for Statement 2: **Distributive Property**
- Statement 3: **\(-4x = 4\)**
- Reason for Statement 3: **Addition Property of Equality**
- Statement 4: **\(x = -1\)**
- Reason for Statement 4: **Division Property of Equality**

So the completed proof is:

| Statements | Reasons |
|------------------------------------------------------|--------------------------------------|
| 1. \(-2(x-4)=2x+12\) | 1. Given |
| 2. \(-2x + 8 = 2x + 12\) | 2. Distributive Property |
| 3. \(-4x = 4\) | 3. Addition Property of Equality |
| 4. \(x = -1\) | 4. Division Property of Equality |

Answer 3

I apologize for the oversight. Let's revise and ensure we provide the correct statements and reasons, including Statement 3.

Here’s the step-by-step solution again, framed within five statements and reasons:

### Given:
\(-2(x-4) = 2x + 12\)

### Proof Steps:
1. **Statement 1:**
\(-2(x-4) = 2x + 12\)
**Reason 1:**
Given

2. **Statement 2:**
\(-2x + 8 = 2x + 12\)
**Reason 2:**
Distributive Property

3. **Statement 3:**
\(-2x - 2x = 12 - 8\) (which simplifies to \(-4x = 4\))
**Reason 3:**
Subtraction Property of Equality (Moving \(2x\) from the right to the left and \(8\) from the left to the right)

4. **Statement 4:**
\( -4x = 4 \)
**Reason 4:**
This is a simplification after applying the subtraction property.

5. **Statement 5:**
\( x = -1 \)
**Reason 5:**
Division Property of Equality (dividing both sides by -4)

### Completed Proof Table

| Statements | Reasons |
|------------------------------------------------------|--------------------------------------|
| 1. \(-2(x-4) = 2x + 12\) | 1. Given |
| 2. \(-2x + 8 = 2x + 12\) | 2. Distributive Property |
| 3. \(-4x = 4\) | 3. Subtraction Property of Equality |
| 4. \(x = -1\) | 4. Division Property of Equality |

Thank you for your patience, and I'm glad to clarify the steps correctly!