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

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

GPT-4o mini · Answer

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

Step 1: $8 + 4 + x^{2} - x^{2} + 17 x = 10 + 2 + 10 x - 4 x^{2} + 7 x + 4 x^{2}$
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: $8 + 4 + 17 x + x^{2} - x^{2} = 10 + 2 + 4 x^{2} - 4 x^{2} + 10 x + 7 x$
Here, it seems terms are correctly rearranged again, but we can simplify the right side: $4 x^{2} - 4 x^{2}$ cancels out, so we should see $10 + 2 + 10 x + 7 x = 12 + 17 x$ .

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

Thus, the mistake is in Step 3 where it incorrectly includes $- x^{2}$ on the right side.

Therefore, the correct answer is: Step 3