Question

which expression is equivalent to $\frac{x}{6} - \frac{3x}{4} + \frac{3x}{2}$?
a $\frac{11x}{12}$
b $\frac{5x}{12}$
c $\frac{11x}{6}$
d $\frac{5x}{6}$

Explanation:

Step1: Find common denominator

The least common denominator of 6, 4, and 2 is 12.

Step2: Rewrite each term

$\frac{x}{6} = \frac{2x}{12}$, $\frac{3x}{4} = \frac{9x}{12}$, $\frac{3x}{2} = \frac{18x}{12}$

Step3: Substitute and compute

$\frac{2x}{12} - \frac{9x}{12} + \frac{18x}{12} = \frac{2x - 9x + 18x}{12} = \frac{11x}{12}$

Answer:

A. $\frac{11x}{12}$