To verify which step contains an error using the Commutative Property of Addition in the given steps, we can analyze each step carefully, focusing particularly on how terms are rearranged or combined.
Let's break down each step:
Step 1: \[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2 \]
In this step, it appears the terms on both sides are being rearranged. The left side simplifies correctly since \( x^2 - x^2 = 0 \).
Step 2: \[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
In this step, the order of addition on both sides remains valid. However, when simplifying, let's look more closely:
- On the left side, combining \( 8 + 4 \) results in \( 12 \).
- The \( x^2 - x^2 \) cancels, resulting in \( 12 + 17x \).
On the right side:
- Combining \( 10 + 2 \) results in \( 12 \).
- The \( 4x^2 - 4x^2 \) cancels, leaving \( 12 + 10x + 7x = 12 + 17x \).
So, the simplifications in both sides seem valid.
Step 3: \[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
This is where we suspect an error. The left side has a \( x^2 \) term while the right side has a \( -x^2 \).
Let's assess the equality: The left side \( 12 + 17x + x^2 \) includes an \( x^2 \) term, while the right side \( 12 - x^2 + 17x \) does not add up as they represent different algebraic expressions.
Thus, Step 3 contains an error regarding the inclusion of the \( x^2 \) term.
Therefore, the correct answer pointing to the mistake is: Step 3.
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