Questions: Which expression is the simplest form of (3(2x-4)-5(x+3))/3 ? A. (11x-27)/3 B. x-9 C. (x-27)/3 D. (x+3)/3

Which expression is the simplest form of (3(2x-4)-5(x+3))/3 ?
A. (11x-27)/3
B. x-9
C. (x-27)/3
D. (x+3)/3

Transcript text: Which expression is the simplest form of $\frac{3(2 x-4)-5(x+3)}{3}$ ? A. $\frac{11 x-27}{3}$ B. $x-9$ C. $\frac{x-27}{3}$ D. $\frac{x+3}{3}$

Solution

Solution Steps

Step 1: Expand the Numerator

First, we need to expand the expression in the numerator:

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

Expanding each term, we have:

\[ 3(2x - 4) = 6x - 12 \]

\[ -5(x + 3) = -5x - 15 \]

Step 2: Simplify the Numerator

Combine the expanded terms:

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

Combine like terms:

\[ (6x - 5x) + (-12 - 15) = x - 27 \]

Step 3: Simplify the Entire Expression

Now, substitute the simplified numerator back into the original expression:

\[ \frac{x - 27}{3} \]

Final Answer

The simplest form of the given expression is:

\[ \boxed{\frac{x - 27}{3}} \]

Thus, the answer is C.

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