To identify the error in your use of the Commutative Property of Addition, let's first clarify what the property states. The Commutative Property of Addition states that the order in which two numbers are added does not change their sum. In other words, \( a + b = b + a \).
Let’s evaluate the expressions step by step to pinpoint where the error might occur in the verification process based on the expressions you've provided.
Original Expression
We start with the left side: \[ 8 + x^2 + 17x - x^2 + 4 \]
Combining Like Terms
- In the left-hand side (LHS):
- Combine \( x^2 \) and \( -x^2 \): \[ 8 + 4 + 17x = 12 + 17x \]
So, the simplified left side becomes: \[ 12 + 17x \]
Right Side Expression
Now, look at the right side: \[ 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \]
Combining Like Terms on the Right
- Combine \( 4x^2 \) and \( -4x^2 \): \[ 10 + 2 + 10x + 7x = 12 + 17x \]
So the simplified right side also becomes: \[ 12 + 17x \]
Comparison
At this point, both sides simplify to: \[ 12 + 17x = 12 + 17x \]
Checking Each Step
Now let's check each statement from your sequence.
-
601.8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2
- This statement isn't necessary for verifying the commutative property since 601.8 is inappropriate in this context. It should not appear based on the original problem format.
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Step 2: 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x:
- It appears you rearranged terms correctly here for the left but reintroduced 4x^2 incorrectly on the right side.
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Step 12 + 17x + x^2 = 12 - x^2 + 17x:
- This statement has an error. The \( x^2 \) terms cancel out, so it should simply state \( 12 + 17x = 12 + 17x \).
Conclusion
The error seems to come from incorporating \( 601.8 \) in your first equation, which is irrelevant. Also, an improper handling and positioning of \( x^2 \) terms appears in some of your steps. Therefore, the structure and some terms present in your equations need reevaluation for clarity and correctness while applying the Commutative Property.
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