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 2
Step 2

Step 1
Step 1

No mistake was made.

Answer 1

To determine which step contains an error in using the Commutative Property of Addition, we should review each step carefully.

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

This step rearranges the terms on both sides. However, both sides should add up correctly:

• Left: \(8 + 4 + 17x + x^2 - x^2 = 12 + 17x\)
• Right: \(10 + 2 + 10x - 4x^2 + 4x^2 = 12 + 10x\)

Step 1 does not equal.

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

When checking this step:

• Left: \(12 + 17x + 0 = 12 + 17x\)
• Right: \(12 + 10x + 7x + 0 = 12 + 17x\)

Step 2 is right.

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

On evaluating:

• Left: \(12 + 17x + 0 = 12 + 17x\)
• Right has an \( -x^2\) on the right that was not accounted for in the left.

This equation is incorrect because there is a difference in the signs regarding \(x^2\).

Thus, the error occurred in Step 3.

The answer is Step 3.