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

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

Sagot :

GinnyAnsweridn
Let's simplify the given expression step by step:

[tex]\[ \frac{5(x-3) - 3(2x + 4)}{9} \][/tex]

### Step 1: Distribute the constants inside the parentheses.
For [tex]\( 5(x-3) \)[/tex]:
[tex]\[ 5(x-3) = 5x - 15 \][/tex]

For [tex]\( 3(2x + 4) \)[/tex]:
[tex]\[ 3(2x + 4) = 6x + 12 \][/tex]

### Step 2: Substitute the distributed terms back into the expression.
[tex]\[ \frac{5x - 15 - (6x + 12)}{9} \][/tex]

### Step 3: Distribute the negative sign and combine like terms in the numerator.
[tex]\[ 5x - 15 - 6x - 12 = (5x - 6x) + (-15 - 12) = -x - 27 \][/tex]

### Step 4: Substitute the simplified numerator back into the fraction.
[tex]\[ \frac{-x - 27}{9} \][/tex]

Thus, the simplest form of the given expression is:
[tex]\[ \boxed{\frac{-x - 27}{9}} \][/tex]

So, the correct answer is:
D. [tex]\(\frac{-x-27}{9}\)[/tex]
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