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Bot GPT 4-o mini 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.