Let's analyze each step one by one to identify if there's any error involving the Commutative Property of Addition:
Step 1:
8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2
This step correctly applies the Commutative Property. The left side simplifies to 12 + 17x (since x^2 - x^2 = 0), and the right side simplifies since -4x^2 + 4x^2 = 0, giving 12 + 10x. So we have:
12 + 17x = 12 + 10x.
Step 2:
8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x
The left-hand side simplifies correctly to 12 + 17x (as the x^2 terms cancel out), and the right side becomes:
10 + 2 = 12 and -4x^2 + 4x^2 cancels out too, leading to:
12 + 10x + 7x = 12 + 17x.
This is also correct.
Step 3:
12 + 17x + x^2 = 12 - x^2 + 17x
Here, there is a mistake. The left side is 12 + 17x (after simplifying), while the right side incorrectly introduces -x^2.
The original equation has x^2 terms that should have canceled out earlier. It should not have a -x^2 term (as x^2 and -x^2 have been canceled out already).
Therefore, the error is in:
Step 3.
So, the correct response to the question is:
Step 3.
1 answer