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

1 answer

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.