To simplify the given expression [tex]\(\frac{3(2x - 4) - 5(x + 3)}{3}\)[/tex], we will follow a step-by-step process.
1. Distribute inside the parenthesis in the numerator:
- Distribute the 3 to the terms inside the first parenthesis:
[tex]\[ 3(2x - 4) = 3 \cdot 2x + 3 \cdot (-4) = 6x - 12 \][/tex]
- Distribute the -5 to the terms inside the second parenthesis:
[tex]\[ -5(x + 3) = -5 \cdot x + (-5) \cdot 3 = -5x - 15 \][/tex]
2. Combine the results of the distributions:
[tex]\[ 3(2x - 4) - 5(x + 3) = (6x - 12) - (5x + 15) \][/tex]
3. Combine like terms:
[tex]\[
6x - 5x - 12 - 15 = x - 27
\][/tex]
4. Construct the simplified expression in the numerator:
[tex]\[
\frac{x - 27}{3}
\][/tex]
Thus, the simplest form of the given expression is:
[tex]\[
\boxed{\frac{x - 27}{3}}
\][/tex]
Hence, the correct option is:
C. [tex]\(\frac{x - 27}{3}\)[/tex]
