Which expression is the simplest form of [tex]\(\frac{5(x-3)-3(2x+4)}{9}\)[/tex]?

A. [tex]\(\frac{-x-27}{9}\)[/tex]
B. [tex]\(\frac{11x-27}{9}\)[/tex]
C. [tex]\(-x-3\)[/tex]
D. [tex]\(\frac{-x-3}{9}\)[/tex]



Answer :

To determine the simplest form of the given expression [tex]\(\frac{5(x-3)-3(2 x+4)}{9}\)[/tex], we start by simplifying the numerator.

### Step-by-Step Simplification:

1. Expand the terms in the numerator:

[tex]\[ 5(x - 3) - 3(2x + 4) \][/tex]

Distribute the coefficients:

[tex]\[ = 5x - 15 - 6x - 12 \][/tex]

2. Combine like terms:

[tex]\[ 5x - 6x - 15 - 12 \][/tex]

Combine the [tex]\(x\)[/tex]-terms and the constant terms:

[tex]\[ = -x - 27 \][/tex]

3. Substitute the simplified numerator back into the fraction:

[tex]\[ \frac{-x - 27}{9} \][/tex]

4. Ensure this fraction is simplified to its simplest form:

The expression [tex]\(\frac{-x - 27}{9}\)[/tex] can be written as [tex]\(\frac{-x}{9} - 3\)[/tex], but the form [tex]\(\frac{-x - 27}{9}\)[/tex] is already one of the choices given.

Now let's compare this to the given options to find the match:

1. Option A: [tex]\(\frac{-x - 27}{9}\)[/tex]

2. Option B: [tex]\(\frac{11x - 27}{9}\)[/tex]

3. Option C: [tex]\(-x - 3\)[/tex]

4. Option D: [tex]\(\frac{-x - 3}{9}\)[/tex]

The simplest form of [tex]\(\frac{5(x-3)-3(2 x+4)}{9}\)[/tex] matches exactly with Option A:

[tex]\[ \boxed{\mathrm{A} \,\, \frac{-x - 27}{9}} \][/tex]