To verify if the steps contain any errors using the Commutative Property of Addition, let's analyze them one by one.
Step 1:
Equation: 8 + 4 + x² - x² + 17x = 10 + 2 + 10x - 4x² + 4x²
Here, we can break it down:
- The left side simplifies to 8 + 4 = 12, and x² - x² cancels out, so it becomes 12 + 17x.
- The right side can be simplified as: 10 + 2 = 12 and 10x - 4x² + 4x² cancels out the terms, resulting in 12 + 10x.
The left side results in 12 + 17x, and the right side results in 12 + 10x. Therefore, the two expressions are not equal, indicating an error.
Step 2:
Equation: 8 + 4 + 17x + x² - x² = 10 + 2 + 4x² - 4x² + 10x + 7x
In this step:
- The left side simplifies again to: 12 + 17x.
- The right side can be simplified as: 10 + 2 = 12 and the cancels out like before: 4x² - 4x² = 0, leading to 12 + 10x + 7x = 12 + 17x.
This step is truly stating the same result as before, which again shows an equality that doesn't hold.
Step 3:
Equation: 12 + 17x + x² = 12 - x² + 17x
- The left side is already simplified to 12 + 17x.
- The right side simplifies as well: 12 + 17x - x².
At this point, x² appears incorrectly on the right side, giving a different arrangement compared to the left side.
Conclusion:
The error occurs primarily in Step 1 and continues through Step 2, since they both lead to incorrect conclusions based on initial simplifications. Therefore, the issue lies in Step 1, where the expressions were noted, showing inequality.
Thus, the correct response is Step 1 contains an error.
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