Let's simplify the given expression step by step:
[tex]\[
\frac{5(x-3) - 3(2x + 4)}{9}
\][/tex]
### Step 1: Distribute the constants inside the parentheses.
For [tex]\( 5(x-3) \)[/tex]:
[tex]\[
5(x-3) = 5x - 15
\][/tex]
For [tex]\( 3(2x + 4) \)[/tex]:
[tex]\[
3(2x + 4) = 6x + 12
\][/tex]
### Step 2: Substitute the distributed terms back into the expression.
[tex]\[
\frac{5x - 15 - (6x + 12)}{9}
\][/tex]
### Step 3: Distribute the negative sign and combine like terms in the numerator.
[tex]\[
5x - 15 - 6x - 12 = (5x - 6x) + (-15 - 12) = -x - 27
\][/tex]
### Step 4: Substitute the simplified numerator back into the fraction.
[tex]\[
\frac{-x - 27}{9}
\][/tex]
Thus, the simplest form of the given expression is:
[tex]\[
\boxed{\frac{-x - 27}{9}}
\][/tex]
So, the correct answer is:
D. [tex]\(\frac{-x-27}{9}\)[/tex]
