Question 9 of 10

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

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



Answer :

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]