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


Responses

Step 1
Step 1

No mistake was made.
No mistake was made.

Step 3
Step 3

Step 2

Answer 1

To identify the error correctly, let's break down the steps and see if we can find a mistake using the Commutative Property of Addition.

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

This step looks fine. It rearranges the terms correctly.

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

This also seems correct. The terms are rearranged but the addition and cancellation of \(x^2\) and \(-x^2\) is done correctly.

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

Here is where the mistake occurs. The left-hand side sums to \(12 + 17x + 0\) (cancelling \(x^2 - x^2 = 0\)), yielding \(12 + 17x\).

On the right-hand side, it has \(12 - x^2 + 17x\).

The equation \(12 + 17x = 12 - x^2 + 17x\) cannot be correct because the \(-x^2\) term is not present on the left side.

Thus, the error occurred in **Step 3** because it incorrectly introduces a \(-x^2\) term which does not belong.

The correct response would be:

**Step 3**