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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 2 Step 2 No mistake was made. No mistake was made. Step 3 Step 3 Step 1 Step 1 Skip to navigation

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To identify the step that contains an error using the Commutative Property of Addition in the verification of the equation, let's analyze each step closely.

  1. Step 1:

    • The expression simplifies correctly, collecting like terms.
    • \(8 + 4 + x^2 - x^2 + 17x\) is correctly rearranged to \(8 + 4 + 17x + x^2 - x^2\).

  2. Step 2:

    • The left-hand side \(10 + 2 + 10x - 4x^2 + 7x\) is rearranged properly.
    • However, notice that on the right-hand side, we have \(10 + 2 + 4x^2 - 4x^2 + 10x + 7x\). The \(4x^2\) and \(-4x^2\) cancel each other out, which makes the right-hand side \(12 + 10x + 7x\) or \(12 + 17x\).
    • So, it seems that \(10 + 2 + 4x^2 - 4x^2 + 10x + 7x\) in step 2 is not showing a mistake, but more of rearrangement.

  3. Step 3:

    • The equation states \(12 + 17x + x^2 = 12 - x^2 + 17x\).
    • This indicates the left side has \(x^2\) while the right side has \(-x^2\), suggesting an imbalance created in this step.

To summarize, the error in verification through the commutative property of addition occurs in Step 3, where the two sides of the equation are not equal due to having \(x^2\) on the left and \(-x^2\) on the right.

So, the correct response is Step 3 contains the error.