Question

Which step contains an error using the Commutative Property of Addition in verifying 8+x2+17x−x2+4=10+4x2+10x−4x2+2+7x?

Step 1: 8+4+x2−x2+17x=10+2+10x−4x2+7x +4x2

Step 2: 8+4+17x+x2−x2=10+2+4x2−4x2+10x+7x

Step 3: 12+17x+x2=12−x2+17x

(1 point)
Responses

No mistake was made.
No mistake was made.

Step 1
Step 1

Step 3
Step 3

Step 2
Step 2

Answer 1

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.