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:

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

2. Statement: -2x + 8 = 2x + 12.
   Reason: Distributive property.

3. Statement: -2x - 2x + 8 = 12.
   Reason: Subtracting 2x from both sides.

4. Statement: -4x + 8 = 12.
   Reason: Combining like terms.

5. Statement: -4x = 4.
   Reason: Subtracting 8 from both sides.

6. Statement: x = -1.
   Reason: Division property of equality (dividing by -4).

So, the completed proof would 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: Combining like terms
5s: -4x = 4
5r: Subtracting 8 from both sides
6s: x = -1
6r: Division property of equality (dividing by -4).

I added a sixth statement and reason to properly conclude the proof.

Answer 2

Take away the 6th statement. The 5th one has division property of equality.

Answer 3

Sure! We can adjust the proof to have only five statements and reasons. Let's recalculate and present it accordingly:

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

2. Statement: -2x + 8 = 2x + 12.
   Reason: Distributive property.

3. Statement: -2x + 8 - 8 = 2x + 12 - 8.
   Reason: Subtracting 8 from both sides.

4. Statement: -2x = 2x + 4.
   Reason: Combining like terms.

5. Statement: -4x = 4.
   Reason: Adding 2x to both sides.

6. Statement: x = -1.
   Reason: Division property of equality.

This solution retains the division property in the concluding proof without introducing a sixth statement. Here is a cleaner version:

1s: -2(x - 4) = 2x + 12
1r: Given
2s: -2x + 8 = 2x + 12
2r: Distributive property
3s: -2x = 2x + 4
3r: Subtracting 8 from both sides
4s: -4x = 4
4r: Adding 2x to both sides
5s: x = -1
5r: Division property of equality.

Let me know if you need any further adjustments!

Answer 4

What's the property for 3?

Answer 5

In step 3 of the proof, where we go from:

Statement 3: \(-2x + 8 - 8 = 2x + 12 - 8\)
Reason 3: Subtraction property of equality.

Here's the updated version of that step:

3s: \(-2x + 8 - 8 = 2x + 12 - 8\)
3r: Subtraction property of equality.

So to summarize the proof properly:

1s: -2(x - 4) = 2x + 12
1r: Given
2s: -2x + 8 = 2x + 12
2r: Distributive property
3s: -2x = 2x + 4
3r: Subtraction property of equality
4s: -4x = 4
4r: Adding 2x to both sides
5s: x = -1
5r: Division property of equality.

Let me know if there's anything else you need!