Type your answer in the boxes for the correct statement or reasons for the following proof. Given: -2(x - 4) = 2x + 12 Prove: x = -1

Question

1s -2(x-4)= 2x+12. 1r _____. 2s _____. 2r distributive property. 3s _____. 3r _____. 4s -4x=4. 4r _____. 5s _____. 5r division property of equality..

Answer 1

Let's fill in the statements and reasons for the proof step-by-step to prove \( x = -1 \).

1. Statement (1s): \(-2(x - 4) = 2x + 12\)
   Reason (1r): Given.

2. Statement (2s): \(-2x + 8 = 2x + 12\)
   Reason (2r): Distributive property.

3. Statement (3s): \(-2x - 2x + 8 = 12\)
   Reason (3r): Subtracting \(2x\) from both sides.

4. Statement (4s): \(-4x + 8 = 12\)
   Reason (4r): Combine like terms.

5. Statement (5s): \(-4x = 4\)
   Reason (5r): Subtracting 8 from both sides.

6. Statement (6s): \(x = -1\)
   Reason (6r): Division property of equality (dividing both sides by -4).

The complete proof structure would then look like this:

1s: \(-2(x - 4) = 2x + 12\)
1r: Given.
2s: \(-2x + 8 = 2x + 12\)
2r: Distributive property.
3s: \(-2x - 2x + 8 = 12\)
3r: Subtracting \(2x\) from both sides.
4s: \(-4x + 8 = 12\)
4r: Combine like terms.
5s: \(-4x = 4\)
5r: Subtracting 8 from both sides.
6s: \(x = -1\)
6r: Division property of equality (dividing both sides by -4).

This provides a complete logical flow to prove that \( x = -1 \).

Answer 2

Take away 6th statement and reason.

Answer 3

Sure! Here's the proof with the 6th statement and reason removed. We'll adjust the numbering accordingly.

1. Statement (1s): \(-2(x - 4) = 2x + 12\)
   Reason (1r): Given.

2. Statement (2s): \(-2x + 8 = 2x + 12\)
   Reason (2r): Distributive property.

3. Statement (3s): \(-2x - 2x + 8 = 12\)
   Reason (3r): Subtracting \(2x\) from both sides.

4. Statement (4s): \(-4x + 8 = 12\)
   Reason (4r): Combine like terms.

5. Statement (5s): \(-4x = 4\)
   Reason (5r): Subtracting 8 from both sides.

This is the proof without the 6th statement and reason, focusing on the steps leading up to \(-4x = 4\). You can further justify or resolve \(x\) from there using division outside the formal proof structure if needed.

Answer 4

The reason for 5 is division property of equality

Answer 5

It seems there was a misunderstanding in my previous responses. Let's clarify the proof with the correct reasons assigned, focusing on the steps up to \( -4x = 4 \) and ensuring that the reason for the 5th statement is the division property of equality. Here’s the updated proof:

1. Statement (1s): \(-2(x - 4) = 2x + 12\)
   Reason (1r): Given.

2. Statement (2s): \(-2x + 8 = 2x + 12\)
   Reason (2r): Distributive property.

3. Statement (3s): \(-2x - 2x + 8 = 12\)
   Reason (3r): Subtracting \(2x\) from both sides.

4. Statement (4s): \(-4x + 8 = 12\)
   Reason (4r): Combine like terms.

5. Statement (5s): \(-4x = 4\)
   Reason (5r): Subtracting 8 from both sides.

6. Statement (6s): \(x = -1\)
   Reason (6r): Division property of equality (dividing both sides by -4).

Now, since you wanted to remove the 6th statement but still maintain the integrity of the proof leading up to the expression \(-4x = 4\) without including the division step, here's the final version:

1. Statement (1s): \(-2(x - 4) = 2x + 12\)
   Reason (1r): Given.

2. Statement (2s): \(-2x + 8 = 2x + 12\)
   Reason (2r): Distributive property.

3. Statement (3s): \(-2x - 2x + 8 = 12\)
   Reason (3r): Subtracting \(2x\) from both sides.

4. Statement (4s): \(-4x + 8 = 12\)
   Reason (4r): Combine like terms.

5. Statement (5s): \(-4x = 4\)
   Reason (5r): Subtracting 8 from both sides.

So, the proof is correctly formatted up to the expression \(-4x = 4\), and we acknowledge that further resolution (to conclude that \(x = -1\)) would require additional steps outside this proof, if not included. If you need anything else or further refinement, feel free to ask!