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 identify the step that contains an error using the Commutative Property of Addition, let's review the steps one by one:

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

This step seems to perform an operation, but let’s break down the right side:
- \(10 + 2 = 12\)
- \( -4x^2 + 4x^2 = 0 \)
- Therefore, it simplifies to \(10 + 2 + 10x + 7x = 12 + 17x\)

So, left side: \(8 + 4 + 17x + x^2 - x^2\) simplifies to \(12 + 17x\).

Thus, Step 1 is correct.

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

On the left:
- \(8 + 4 = 12\)
- The \(x^2 - x^2\) cancels out, giving us \(12 + 17x\).

On the right:
- \(10 + 2 = 12\)
- The \(4x^2 - 4x^2\) cancels out, leaving \(12 + 10x + 7x = 12 + 17x\).

So, Step 2 is also correct.

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

Here, the left side is fine, \(12 + 17x + x^2\).

However, the right side \(12 - x^2 + 17x\) is incorrect because it does not account for the \(x^2\) present on the left side.

So, the error occurs in **Step 3**.

The answer is **Step 3** contains the error.