To determine which expressions are equivalent to [tex]\(-f - 5(2f - 3)\)[/tex], let's simplify the given expression step-by-step.
1. Distribute the 5: Start by distributing the 5 across the terms inside the parentheses:
[tex]\[
-f - 5(2f - 3) = -f - 5 \cdot 2f + 5 \cdot 3
\][/tex]
2. Multiply: Perform the multiplication:
[tex]\[
-f - 10f + 15
\][/tex]
3. Combine like terms: Combine the terms involving [tex]\(f\)[/tex]:
[tex]\[
-f - 10f = -11f
\][/tex]
So the expression simplifies to:
[tex]\[
-11f + 15
\][/tex]
Now that we have the simplified form of the expression, let's compare it to the given answer choices:
- (A) [tex]\(-11f - 3\)[/tex]: This expression differs from the simplified form [tex]\(-11f + 15\)[/tex]. The constant term here is [tex]\(-3\)[/tex] instead of [tex]\(15\)[/tex].
- (B) [tex]\(-11f + 15\)[/tex]: This expression matches our simplified form exactly.
- (C) None of the above: This option would be correct if none of the provided expressions matched our simplified form.
Based on the simplification and comparisons, the correct equivalent expression is [tex]\(-11f + 15\)[/tex].
Therefore, the answer is:
- [tex]\(\boxed{B}\)[/tex]
