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 3
Step 3

Step 1
Step 1

No mistake was made.
No mistake was made.

Step 2

Answer 1

To determine which step contains an error using the Commutative Property of Addition, let's analyze each step systematically.

**Step 1:**
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2 \]
- On the left side: \( x^2 - x^2 \) cancels out.
- On the right side: \( -4x^2 + 4x^2 \) also cancels out.
This step appears correct.

**Step 2:**
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
- The left side simplifies to \( 12 + 17x \).
- The right side simplifies to \( 12 + 10x + 7x \) which equals \( 12 + 17x \).
This step also appears correct.

**Step 3:**
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
- The left side is \( 12 + 17x + x^2 \).
- The right side is \( 12 - x^2 + 17x \).

The issue here is that the term \( x^2 \) on the left side is incorrectly stated as \( -x^2 \) on the right side. The equation is not balanced due to this inconsistency.

Therefore, the error is found in:

**Step 3.**