High School

Select all expressions that are equivalent to \(-\frac{3}{4}(32 - 4f)\):

A. 24 - 3f
B. 3f - 24
C. -24 + 3f
D. 8 - f
E. 3(-8 + f)

Answer :

Final answer:

The expressions equivalent to -3/4( 32 - 4f) are 3f - 24, -24 + 3f, and 3(-8 +f), as they all simplify to the same value.

Explanation:

The expressions equivalent to -3/4( 32 - 4f) are obtained by simplifying the given expression. Firstly, distribute -3/4 within the parentheses which yields -24 + 3f.

Now, compare this simplified expression to the options given:

  • 24 - 3f is not equivalent because the signs are opposite.
  • 3f - 24 is equivalent because it's merely a rearrangement of terms.
  • -24 + 3f is equivalent because it's exactly the same.
  • 8 - f is not equivalent.
  • 3(-8 +f) is equivalent because, when simplified, it gives -24 + 3f.

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