To identify the step containing an error using the Commutative Property of Addition, we need to analyze each step to see if the simplifications and order of terms are applied correctly.
Step 1: \( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
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The left side simplifies as follows:
- \( 8 + 4 = 12 \)
- \( x^2 - x^2 = 0 \)
- So, \( 12 + 17x \).
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The right side also needs to be simplified:
- Combine like terms: \( 10 + 2 = 12 \) and \( 10x + 7x = 17x \).
- The terms involving \( x^2 \): \( -4x^2 + 4x^2 = 0 \).
So, the right side simplifies to \( 12 + 17x \).
Thus, Step 1 is correct.
Step 2: \( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
- The left side simplifies likewise:
- \( 8 + 4 = 12 \),
- \( 17x + 0 = 17x \).
So, the left side simplifies to \( 12 + 17x \).
- The right side:
- \( 10 + 2 = 12 \),
- Combine like terms: \( 10x + 7x = 17x \),
- And \( 4x^2 - 4x^2 = 0 \).
So the right side also simplifies to \( 12 + 17x \).
Thus, Step 2 is correct.
Step 3: \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
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On the left side, we have \( 12 + 17x + x^2 \).
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On the right side, \( 12 - x^2 + 17x \) suggests a term \( -x^2 \).
In Step 3, the left and right sides are not equal due to the presence of the \( x^2 \) term on the left side and the \( -x^2 \) term on the right side:
12 + 17x + x^2 ≠ 12 - x^2 + 17x
This inconsistency indicates that Step 3 is erroneous.
Therefore, the incorrect step is Step 3.
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