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Reorder the terms using the commutative property: 9 + 4x - 7 - 2x = 9 - 7 + 4x - 2x.

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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.

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