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 Step 3 Step 3 Step 2 Step 2 Step 1 Step 1 No mistake was made.

Answer 1

To verify which step contains an error using the Commutative Property of Addition, let's examine each step closely.

### Given Expression:
Verify:
\[ 8 + x^2 + 17x - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \]

### Steps
**Step 1:**
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]

**Step 2:**
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]

**Step 3:**
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]

### Analyzing Each Step
1. **Step 1:** Rearrangement of terms is made but the operations look appropriate, as they group like terms together.
2. **Step 2:** Again grouping like terms, however, we notice in the right side, \(4x^2\) and \(-4x^2\) should cancel out.
3. **Step 3:** The left side simplifies correctly to \(12 + 17x\). On the right side, having \(-x^2 + 17x\) seems suspicious since there’s not a corresponding \(x^2\) term on the left.

### Identifying the Error
The critical error seems to be in **Step 3** since it incorrectly implies:
- The left side simplifies to \(12 + 17x + x^2\) while the right side simplifies to \(12 + 17x\) without any \(x^2\) term present.

Thus, the answer is:
**Step 3** contains the error.