Final answer:
The commutative property allows the rearrangement of terms in the expression 9 + 4x - 7 - 2x to get 9 - 7 + 4x - 2x. After combining like terms, the expression is simplified to 2 + 2x. Checking for reasonableness can be done by comparing results from the original and simplified expressions for any value of x.
Step-by-step explanation:
When applying the commutative property of addition, which allows us to rearrange the terms in a sum, we can reorder the expression 9 + 4x - 7 - 2x to 9 - 7 + 4x - 2x. After reordering, we use the property to eliminate terms and simplify the algebra by combining like terms. Here's the step-by-step process:
- Combine constant terms: (9 - 7) = 2.
- Combine like variables: (4x - 2x) = 2x.
- The simplified expression is: 2 + 2x.
To check if the answer is reasonable, you can substitute any value for x and see if the original equation and the simplified one yield the same result.