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

No mistake was made.
No mistake was made.

Step 2
Step 2

Step 3
Step 3

Step 1

Answer 1

To verify which step contains an error using the Commutative Property of Addition, let's look at each step more closely. The Commutative Property states that the order in which you add numbers does not change the sum.

**Step 1:**
\[
8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2
\]
This step seems correct. The terms are rearranged properly, and since \(x^2 - x^2\) cancels out, it works out.

**Step 2:**
\[
8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x
\]
This step, however, has a mistake. Specifically, you have \(4x^2 - 4x^2\) which cancels out, but the addition of \(10x + 7x\) should combine to \(17x\), which is not done correctly. Instead, you have both \(10x\) and \(7x\) without properly simplifying.

**Step 3:**
\[
12 + 17x + x^2 = 12 - x^2 + 17x
\]
This step introduces an error as well as it suggests that \(x^2 + 0 = -x^2\) when essentially both should simplify to just \(12 + 17x\) on both sides after correctly simplifying.

So, the primary error lies in **Step 2** where the terms involving \(4x^2\) and \(10x+7x\) are not simplified correctly.

The answer is: **Step 2**.