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.