Let's solve the expression [tex]\(3(-3 n + 7) - 8(6 p - 9 q)\)[/tex] step-by-step by applying the distributive property.
First, distribute the constants 3 and -8 inside their respective parentheses.
### Step 1: Distribute 3 in [tex]\(3(-3 n + 7)\)[/tex]
- [tex]\(3 \cdot -3n = -9n\)[/tex]
- [tex]\(3 \cdot 7 = 21\)[/tex]
So, [tex]\(3(-3n + 7)\)[/tex] simplifies to [tex]\(-9n + 21\)[/tex].
### Step 2: Distribute -8 in [tex]\(-8(6 p - 9 q)\)[/tex]
- [tex]\(-8 \cdot 6p = -48p\)[/tex]
- [tex]\(-8 \cdot -9q = 72q\)[/tex]
So, [tex]\(-8(6p - 9q)\)[/tex] simplifies to [tex]\(-48p + 72q\)[/tex].
### Step 3: Combine the results from Step 1 and Step 2
Now we combine [tex]\(-9n + 21\)[/tex] and [tex]\(-48p + 72q\)[/tex]:
[tex]\[
3(-3n + 7) - 8(6p - 9q) = (-9n + 21) + (-48p + 72q)
\][/tex]
This simplifies to:
[tex]\[
-9n + 21 - 48p + 72q
\][/tex]
Therefore, the correct answer from the given options is:
[tex]\[ \boxed{-9n + 21 - 48p + 72q} \][/tex]
Which corresponds to:
Option 4) [tex]\(-9 n + 21 - 48 p + 72 q\)[/tex]
