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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+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

A. Step 2
B. Step 3
C. No mistake was made
D. Step 1

1 answer

To identify the error using the Commutative Property of Addition in verifying the equation, we will evaluate each step carefully:

  1. Step 1:
    • The left side: \( 8 + 4 + x^2 - x^2 + 17x \) combines to \( 12 + 17x \) since \( x^2 - x^2 = 0 \).
    • The right side: \( 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \) simplifies to \( 12 + 10x + (4x^2 - 4x^2) = 12 + 10x \).
    • This is incorrect because \( 12 + 17x \) does not equal \( 12 + 10x \).

So, there is indeed a mistake in Step 1.

  1. Step 2:
    • The left side: \( 8 + 4 + 17x + x^2 - x^2 \) is \( 12 + 17x \) (again, \( x^2 - x^2 = 0 \)).
    • The right side: \( 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \) simplifies to \( 12 + 10x + 0 + 17x = 12 + 17x \).
    • However, it should have been \( 12 + 10x \) without combining terms incorrectly.

This also indicates an error, but more regarding the prior step.

  1. Step 3:
    • The left side remains \( 12 + 17x \), and we can check the right side: at this state, error accumulates from Step 1 and 2, mismatching terms.

Since the first error has propagated, the original incorrect simplification stands out among the choices highlighted.

The mistakes in the context appear predominantly highlighted from Step 1 which cascaded through subsequent reasoning.

Thus, the answer is: D. Step 1.