Question

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

Step 2
Step 1
no mistake was made
step 3

Answer 1

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:**
\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)

- The left side simplifies as follows:
- \( 8 + 4 = 12 \)
- \( x^2 - x^2 = 0 \)
- So, \( 12 + 17x \).

- 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.

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**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.

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**Step 3:**
\( 12 + 17x + x^2 = 12 - x^2 + 17x \)

- On the left side, we have \( 12 + 17x + x^2 \).

- 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**.