Type your answer in the boxes for the correct statement or reasons for the following proof.

Question

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

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 2

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

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!