Which step contains an error using the Commutative Property of Addition in verifying 8+x2+17x−x2+4=10+4x2+10x−4x2+2+7x ?

Question

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 identify the error in the steps using the Commutative Property of Addition, let's analyze each step carefully.

Step 1:
The original expression is transformed to:
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]
This step appears to correctly rearrange the terms according to the Commutative Property of Addition, which allows for changing the order of addition.

Step 2:
Now the equation is expressed as:
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
Again, this step seems to follow the rules of addition.

Step 3:
This step simplifies it to:
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
Here, we need to analyze for any simplification errors. The left side is correctly simplified to \( 12 + 17x \) (since \( x^2 - x^2 = 0 \)).
However, on the right side, \( -x^2 \) should not appear because \( 4x^2 - 4x^2 = 0 \) and should just reduce to \( 12 + 17x \).

Thus, in Step 3, there is an inconsistency since it introduces \( -x^2 \) on the right side, which arose incorrectly since both terms involving \( x^2 \) should cancel out.

Therefore, the step that contains an error is:

Step 3