Answer :
Let's work through the problem to find the expressions that are equivalent to [tex]\(-\frac{3}{4}(32-4f)\)[/tex].
1. Distribute the [tex]\(-\frac{3}{4}\)[/tex]:
- First, apply the distributive property: Multiply [tex]\(-\frac{3}{4}\)[/tex] by each term inside the parentheses.
- [tex]\(-\frac{3}{4} \times 32 = -24\)[/tex]
- [tex]\(-\frac{3}{4} \times (-4f) = 3f\)[/tex]
2. Combine the results:
- When you combine the terms from the distribution, you get: [tex]\(-24 + 3f\)[/tex]
Now let's compare this result to each of the choices given:
- [tex]$24-3f$[/tex]:
- This is not equivalent because the signs and terms do not match [tex]\(-24 + 3f\)[/tex].
- [tex]$3f-24$[/tex]:
- This expression is equivalent since it's simply reorganizing the terms of [tex]\(-24 + 3f\)[/tex] to [tex]\(3f - 24\)[/tex].
- [tex]$-24+3f$[/tex]:
- This is exactly our result, so it is equivalent.
- [tex]$8-f$[/tex]:
- This is not equivalent because both the signs and coefficients do not match [tex]\(-24 + 3f\)[/tex].
- [tex]$3(-8+f)$[/tex]:
- Let's simplify this to see if it matches:
- Distribute the 3: [tex]\(3 \times (-8) + 3 \times f = -24 + 3f\)[/tex]
- This expression is indeed equivalent to [tex]\(-24 + 3f\)[/tex].
So, the expressions that are equivalent to [tex]\(-\frac{3}{4}(32-4f)\)[/tex] are:
- [tex]$3f-24$[/tex]
- [tex]$-24+3f$[/tex]
- [tex]$3(-8+f)$[/tex]
1. Distribute the [tex]\(-\frac{3}{4}\)[/tex]:
- First, apply the distributive property: Multiply [tex]\(-\frac{3}{4}\)[/tex] by each term inside the parentheses.
- [tex]\(-\frac{3}{4} \times 32 = -24\)[/tex]
- [tex]\(-\frac{3}{4} \times (-4f) = 3f\)[/tex]
2. Combine the results:
- When you combine the terms from the distribution, you get: [tex]\(-24 + 3f\)[/tex]
Now let's compare this result to each of the choices given:
- [tex]$24-3f$[/tex]:
- This is not equivalent because the signs and terms do not match [tex]\(-24 + 3f\)[/tex].
- [tex]$3f-24$[/tex]:
- This expression is equivalent since it's simply reorganizing the terms of [tex]\(-24 + 3f\)[/tex] to [tex]\(3f - 24\)[/tex].
- [tex]$-24+3f$[/tex]:
- This is exactly our result, so it is equivalent.
- [tex]$8-f$[/tex]:
- This is not equivalent because both the signs and coefficients do not match [tex]\(-24 + 3f\)[/tex].
- [tex]$3(-8+f)$[/tex]:
- Let's simplify this to see if it matches:
- Distribute the 3: [tex]\(3 \times (-8) + 3 \times f = -24 + 3f\)[/tex]
- This expression is indeed equivalent to [tex]\(-24 + 3f\)[/tex].
So, the expressions that are equivalent to [tex]\(-\frac{3}{4}(32-4f)\)[/tex] are:
- [tex]$3f-24$[/tex]
- [tex]$-24+3f$[/tex]
- [tex]$3(-8+f)$[/tex]
