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

No mistake was made.
No mistake was made.

Step 2
Step 2

Step 3
Step 3

Step 1
Step 1
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Answer 1

To identify the step that contains an error using the Commutative Property of Addition, let's analyze each step in detail:

**Step 1:**
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]
- This step correctly organizes the terms.

**Step 2:**
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
- In the left-hand side, \( x^2 - x^2 \) correctly cancels out. However, we need to verify the right-hand side:
- On the right side, \( 10 + 2 + (10x + 7x) + (4x^2 - 4x^2) \) should combine as follows: \( 10 + 2 + 10x + 7x \) which simplifies to \( 12 + 17x \), and the \( 4x^2 - 4x^2 \) cancels to 0.
- Therefore, the right-hand side is indeed \( 12 + 17x \), just like the left side.

**Step 3:**
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
- This is where we find the error. The left side has \( x^2 \) and the right side has \( -x^2 \). These terms are not equivalent.

From the analysis, the error occurs in Step 3 since it presents a false equivalence of \( x^2 \) and \( -x^2 \) which is not valid.

Therefore, the answer is **Step 3**.