Let's simplify the given expression step-by-step.
The original expression is:
[tex]\[
\frac{3(2x - 4) - 5(x + 3)}{3}
\][/tex]
Step 1: Distribute the numbers inside the parentheses.
First, we'll distribute [tex]\( 3 \)[/tex] through [tex]\( (2x - 4) \)[/tex]:
[tex]\[
3(2x - 4) = 3 \cdot 2x - 3 \cdot 4 = 6x - 12
\][/tex]
Next, we'll distribute [tex]\( -5 \)[/tex] through [tex]\( (x + 3) \)[/tex]:
[tex]\[
-5(x + 3) = -5 \cdot x - 5 \cdot 3 = -5x - 15
\][/tex]
Step 2: Combine these results.
We now combine [tex]\( 6x - 12 \)[/tex] and [tex]\( -5x - 15 \)[/tex]:
[tex]\[
6x - 12 - 5x - 15
\][/tex]
Step 3: Combine like terms.
Combining like terms:
[tex]\[
6x - 5x = x
\][/tex]
[tex]\[
-12 - 15 = -27
\][/tex]
So, the expression simplifies to:
[tex]\[
x - 27
\][/tex]
Step 4: Put the simplified expression over the original denominator.
Now, we put this simplified expression over the original denominator [tex]\( 3 \)[/tex]:
[tex]\[
\frac{x - 27}{3}
\][/tex]
Step 5: Divide each term by 3.
Dividing each term in the numerator by [tex]\( 3 \)[/tex]:
[tex]\[
\frac{x}{3} - \frac{27}{3} = \frac{x}{3} - 9
\][/tex]
Therefore, the simplified expression for [tex]\(\frac{3(2x - 4) - 5(x + 3)}{3}\)[/tex] is:
[tex]\[
\frac{x - 27}{3}
\][/tex]
So the answer is:
C. [tex]\(\frac{x - 27}{3}\)[/tex]
