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 1

Step 2
Step 2

Step 3
Step 3

No mistake was made.

Answer 1

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

### Original Equation:
The original equation is:
\[ 8 + x^2 + 17x - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \]

### Let's break down the steps:

#### Step 1:
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]
- In this step, the left-hand side is rearranged, and the right-hand side is also rearranged.
- The left side simplifies correctly to \( 12 + 17x \) since \( x^2 - x^2 = 0 \).
- On the right side, combining terms like \( -4x^2 + 4x^2 \) gives 0, resulting in \( 12 + 10x + 7x = 12 + 17x \).
- **This step seems correct.**

#### Step 2:
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
- Rearranging here with the same grouping:
- The left side still simplifies to \( 12 + 17x \).
- The right side simplifies to \( 12 + 17x \) as well.
- **This step appears correct.**

#### Step 3:
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
- This step claims that \( 12 + 17x + x^2 = 12 - x^2 + 17x \).
- However, \( x^2 \) on the left side doesn't equal \( -x^2 \) on the right side.
- Combining like terms correctly, an error is present here because both sides are not equal.

### Conclusion:
The error appears in **Step 3**, where the equality fails due to incorrect handling of \( x^2 \).

Thus, the answer is: **Step 3**.