Which step contains an error using the Commutative Property of Addition in verifying

Question

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Step 1:
Step 2:
Step 3:
(1 point)
8 + + 17x x2 − x2 + 4 = 10 + 4x2 + 10x − 4x2 + 2 + 7x
8 + 4 + x2 − x2 + 17x = 10 + 2 + 10x − 4x2 + 7x + 4x2
8 + 4 + 17x + x2 − x2 = 10 + 2 + 4x2 − 4x2 + 10x + 7x
12 + 17x + x2 = 12 − x2 + 17x
Step 1
Step 3
No mistake was made.
Step 2

Answer 1

To determine which step contains an error using the Commutative Property of Addition, let's analyze each step:

Step 1:
\( 8 + 17x + x^2 - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \)

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

Step 3:
\( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)

Final step:
\( 12 + 17x + x^2 = 12 - x^2 + 17x \)

Now, let's break down what's happening in each step:

• In Step 1, all terms are correctly stated, but note the arrangement on the right side.
• In Step 2, there's a rearrangement, but it looks like both sides are attempting to simplify to follow a similar structure. All terms are present.
• In Step 3, no terms are omitted, and the arrangement maintains the same structure.

Now examining the simplification:

• The left side in Step 3 simplifies to: \( 12 + 17x \) (since \( x^2 - x^2 = 0 \)).
• The right side in Step 3 simplifies incorrectly: \( 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \) should give \( 12 + 17x \).

Thus, Step 2 contains an error in adding and organizing the terms correctly. It mixes them and doesn’t appropriately combine like terms.

The answer is Step 2.