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

Question

.(1 point)
Responses

18+5f
18 plus 5 f

14+22f
14 plus 22 f

14+7f
14 plus 7 f

21f
21 f

Answer 1

To apply the Commutative Property, we can rearrange the terms in the expression \(8 + 9f - 2 + 6f - 8f - 4 + 12\) to group like terms together.

Let's first rearrange the constants and the 'f' terms:

1. Group the constants: \(8 - 2 - 4 + 12\)
2. Group the 'f' terms: \(9f + 6f - 8f\)

Now, let's simplify each group:

• For the constants:
  • \(8 - 2 = 6\)
  • \(6 - 4 = 2\)
  • \(2 + 12 = 14\)

So, the sum of the constants is \(14\).

• For the 'f' terms:
  • \(9f + 6f = 15f\)
  • \(15f - 8f = 7f\)

So, the sum of the 'f' terms is \(7f\).

Now, combine the results:

The final expression is \(14 + 7f\).

The equivalent expression is 14 + 7f.

Therefore, the correct response is: 14 plus 7 f.