Answer
$= \frac{11x}{24}$
Work Step by Step
1) Find a common denominator: multiply the first fraction by $12$, the second fraction by $6$, and the third fraction by $4$; leave the last fraction unchanged in order to obtain a common denominator of $24$
$\frac{1}{2}x + \frac{3}{4}x - \frac{5}{6}x + \frac{1}{24}x$
$= \frac{1x}{2} + \frac{3x}{4} - \frac{5x}{6} + \frac{x}{24}$
$= \frac{x(12)}{24} + \frac{3x(6)}{24} - \frac{5x(4)}{24} + \frac{x}{24}$
$= \frac{12x}{24} + \frac{18x}{24} - \frac{20x}{24} + \frac{x}{24}$
$= \frac{12x+18x-20x+x}{24}$
$= \frac{30x-19x}{24}$
$= \frac{11x}{24}$
