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

A. [tex] \frac{11x-27}{3} \)

B. [tex] x-9 \)

C. [tex] \frac{x-27}{3} \)

D. [tex] \frac{x+3}{3} \)

Sagot :

GinnyAnsweridn
Let's simplify the given expression step-by-step.

The original expression is:

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

Step 1: Distribute the numbers inside the parentheses.

First, we'll distribute [tex]\( 3 \)[/tex] through [tex]\( (2x - 4) \)[/tex]:

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

Next, we'll distribute [tex]\( -5 \)[/tex] through [tex]\( (x + 3) \)[/tex]:

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

Step 2: Combine these results.

We now combine [tex]\( 6x - 12 \)[/tex] and [tex]\( -5x - 15 \)[/tex]:

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

Step 3: Combine like terms.

Combining like terms:

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

[tex]\[ -12 - 15 = -27 \][/tex]

So, the expression simplifies to:

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

Step 4: Put the simplified expression over the original denominator.

Now, we put this simplified expression over the original denominator [tex]\( 3 \)[/tex]:

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

Step 5: Divide each term by 3.

Dividing each term in the numerator by [tex]\( 3 \)[/tex]:

[tex]\[ \frac{x}{3} - \frac{27}{3} = \frac{x}{3} - 9 \][/tex]

Therefore, the simplified expression for [tex]\(\frac{3(2x - 4) - 5(x + 3)}{3}\)[/tex] is:

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

So the answer is:

C. [tex]\(\frac{x - 27}{3}\)[/tex]
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