Apply the Commutative Property to generate an expression equivalent to 8+9f−2+6f−8f−4+12

Question

.(1 point)
Responses

21f
21 f

18+5f
18 plus 5 f

14+22f
14 plus 22 f

14+7f

Answer 1

To apply the Commutative Property and simplify the expression \(8 + 9f - 2 + 6f - 8f - 4 + 12\), we will first rearrange the terms and then combine like terms.

1. Rearranging the expression:
   \(8 - 2 - 4 + 12 + 9f + 6f - 8f\)

2. Combining the constant terms:
   \(8 - 2 = 6\)
   \(6 - 4 = 2\)
   \(2 + 12 = 14\)

3. Combining the \(f\) terms:
   \(9f + 6f - 8f = (9 + 6 - 8)f = 7f\)

Now we can combine both results: \[ 14 + 7f \]

Thus, the equivalent expression is \(14 + 7f\).

The correct response is: 14 + 7f