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 2
Step 2

Step 3
Step 3

No mistake was made.
No mistake was made.

Step 1
Step 1
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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

Let's analyze each step one by one to identify if there's any error involving the Commutative Property of Addition:

**Step 1:**
8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2
This step correctly applies the Commutative Property. The left side simplifies to 12 + 17x (since x^2 - x^2 = 0), and the right side simplifies since -4x^2 + 4x^2 = 0, giving 12 + 10x. So we have:
12 + 17x = 12 + 10x.

**Step 2:**
8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x
The left-hand side simplifies correctly to 12 + 17x (as the x^2 terms cancel out), and the right side becomes:
10 + 2 = 12 and -4x^2 + 4x^2 cancels out too, leading to:
12 + 10x + 7x = 12 + 17x.

This is also correct.

**Step 3:**
12 + 17x + x^2 = 12 - x^2 + 17x
Here, there is a mistake. The left side is 12 + 17x (after simplifying), while the right side incorrectly introduces -x^2.

The original equation has x^2 terms that should have canceled out earlier. It should not have a -x^2 term (as x^2 and -x^2 have been canceled out already).

Therefore, the error is in:

**Step 3.**

So, the correct response to the question is:

**Step 3.**