To determine which step contains an error using the Commutative Property of Addition, let's analyze each step:
Original Equation:
The original equation is: \[ 8 + x^2 + 17x - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \]
Let's break down the steps:
Step 1:
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]
- In this step, the left-hand side is rearranged, and the right-hand side is also rearranged.
- The left side simplifies correctly to \( 12 + 17x \) since \( x^2 - x^2 = 0 \).
- On the right side, combining terms like \( -4x^2 + 4x^2 \) gives 0, resulting in \( 12 + 10x + 7x = 12 + 17x \).
- This step seems correct.
Step 2:
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
- Rearranging here with the same grouping:
- The left side still simplifies to \( 12 + 17x \).
- The right side simplifies to \( 12 + 17x \) as well.
- This step appears correct.
Step 3:
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
- This step claims that \( 12 + 17x + x^2 = 12 - x^2 + 17x \).
- However, \( x^2 \) on the left side doesn't equal \( -x^2 \) on the right side.
- Combining like terms correctly, an error is present here because both sides are not equal.
Conclusion:
The error appears in Step 3, where the equality fails due to incorrect handling of \( x^2 \).
Thus, the answer is: Step 3.
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