Question

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 2
Step 2

Step 1
Step 1

No mistake was made.
No mistake was made.

Step 3

Answer 1

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

Step 1:
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]

In this step, the left side simplifies to \( 12 + 17x \) since \( x^2 - x^2 \) cancels out. The right side simplifies to \( 12 + 10x + 7x = 12 + 17x \). Therefore, Step 1 is correct.

Step 2:
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]

Again, on the left side, \( x^2 - x^2 \) cancels out, resulting in \( 12 + 17x \). On the right side, \( 4x^2 - 4x^2 \) also cancels out, and we have \( 10 + 2 + 10x + 7x = 12 + 17x \). Therefore, Step 2 is also correct.

Step 3:
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]

The left side is \( 12 + 17x + x^2 \). The right side needs careful examination. It has \( 12 - x^2 + 17x \). Here lies the issue, as the left side has an \( x^2 \) while the right side has a \(-x^2\). These are not equal, indicating a mistake has occurred.

Thus, the step that contains an error is Step 3.

The correct response is: Step 3.