Which step contains an error using the Commutative Property of Addition in verifying 8+x2+17x−x2+4=10+4x2+10x−4x2+2+7x ?%0D%0A%0D%0AStep 1: 8+4+x2−x2+17x=10+2+10x−4x2+7x +4x2 %0D%0A%0D%0AStep 2: 8+4+17x+x2−x2=10+2+4x2−4x2+10x+7x %0D%0A%0D%0AStep 3: 12+17x+x2=12−x2+17x %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AStep 3%0D%0AStep 3%0D%0A%0D%0AStep 2%0D%0AStep 2%0D%0A%0D%0AStep 1%0D%0AStep 1%0D%0A%0D%0ANo mistake was made.

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 ?%0D%0A%0D%0AStep 1:  8+4+x2−x2+17x=10+2+10x−4x2+7x +4x2 %0D%0A%0D%0AStep 2:  8+4+17x+x2−x2=10+2+4x2−4x2+10x+7x %0D%0A%0D%0AStep 3:  12+17x+x2=12−x2+17x %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AStep 3%0D%0AStep 3%0D%0A%0D%0AStep 2%0D%0AStep 2%0D%0A%0D%0AStep 1%0D%0AStep 1%0D%0A%0D%0ANo mistake was made.

GPT-4o mini · Answer

To find the step that contains an error while applying the Commutative Property of Addition, we can analyze each step.

Step 1: \( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)

In this step, the terms on both sides appear to be rearranged correctly.

Step 2: \( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)

This seems fine as well because \(x^2 - x^2\) cancels out, leaving \(8 + 4 + 17x\) on the left and \(10 + 2 + 10x + 7x\) on the right.

Step 3: \( 12 + 17x + x^2 = 12 - x^2 + 17x \)

This is the step that contains an error. The left side correctly combines to \(12 + 17x\), but on the right side, after canceling \(4x^2 - 4x^2\) in Step 2, it should maintain \(12 + 17x\) instead of \(12 - x^2 + 17x\). The presence of \(-x^2\) in this context is inconsistent and incorrectly modifies the equation.

Therefore, the error is in Step 3.