To determine which expression is the simplest form of [tex]\(\frac{5(x-3)-3(2x+4)}{9}\)[/tex], let's work through the problem step-by-step.
1. Distribute the constants inside the parentheses:
- [tex]\( 5(x - 3) \)[/tex] becomes [tex]\( 5x - 15 \)[/tex]
- [tex]\(-3(2x + 4)\)[/tex] becomes [tex]\(-6x - 12\)[/tex]
This gives us:
[tex]\[
\frac{5(x - 3)-3(2x+4)}{9} = \frac{5x - 15 - 6x - 12}{9}
\][/tex]
2. Combine like terms in the numerator:
- [tex]\( 5x - 6x \)[/tex] simplifies to [tex]\(-x\)[/tex]
- [tex]\(-15 - 12\)[/tex] simplifies to [tex]\(-27\)[/tex]
So, the expression becomes:
[tex]\[
\frac{5x - 15 - 6x - 12}{9} = \frac{-x - 27}{9}
\][/tex]
3. Check the given options to find the simplest form:
- Option A: [tex]\(\frac{-x - 27}{9}\)[/tex]
- Option B: [tex]\(-x - 3\)[/tex]
- Option C: [tex]\(\frac{11x - 27}{9}\)[/tex]
- Option D: [tex]\(\frac{-x - 3}{9}\)[/tex]
By comparing our simplified expression [tex]\(\frac{-x - 27}{9}\)[/tex] with the given options, we see that Option A matches our result.
Therefore, the simplest form of the given expression is:
[tex]\[
\boxed{\frac{-x - 27}{9}}
\][/tex]
