Answer
$x=\displaystyle \frac{35}{2}$
$x=\displaystyle -\frac{25}{2}$
Work Step by Step
$\displaystyle 8+5| \frac{1}{3}x-\frac{5}{6}|=33$
$\displaystyle 5|\frac{1}{3}x-\frac{5}{6}|=33-8=25$
$\displaystyle |\frac{1}{3}x-\frac{5}{6}|=25/5=5$
We split the absolute value equation into the positive and negative:
$\displaystyle \frac{1}{3}x-\frac{5}{6}=5$
$\displaystyle \frac{1}{3}x=\frac{5*6}{6}+\frac{5}{6}=\frac{35}{6}$
$x=\displaystyle \frac{35*3}{6}=\frac{35}{2}$
$\displaystyle \frac{1}{3}x-\frac{5}{6}=-5$
$\displaystyle \frac{1}{3}x=-\frac{5*6}{6}+\frac{5}{6}=-\frac{25}{6}$
$\displaystyle x=-\frac{25*3}{6}=-\frac{25}{2}$
