Which step contains an error using the Commutative Property of Addition in verifying 8+x2+17x−x2+4=10+4x2+10x−4x2+2+7x ?

Question

Step 1: 8+4+x2−x2+17x=10+2+10x−4x2+7x +4x2
Step 2: 8+4+17x+x2−x2=10+2+4x2−4x2+10x+7x
Step 3: 12+17x+x2=12−x2+17x
(1 point) Responses
Step 1
Step 2
Step 3
No mistake was made.

Answer 1

To verify where the error occurred using the Commutative Property of Addition, let's examine each step closely:

Step 1: \( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
Here, we have terms rearranged on both sides. We need to ensure that the addition of the terms is consistent on both sides.

Step 2: \( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
Here, it seems terms are correctly rearranged again, but we can simplify the right side: \( 4x^2 - 4x^2 \) cancels out, so we should see \( 10 + 2 + 10x + 7x = 12 + 17x \).

Step 3: \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Here is where the error is. The left side should be \( 12 + 17x + 0 = 12 + 17x \) but on the right side it's incorrectly stated as \( 12 - x^2 + 17x\).

Thus, the mistake is in Step 3 where it incorrectly includes \( -x^2 \) on the right side.

Therefore, the correct answer is: Step 3