Answer
$\displaystyle x=\frac{11}{8}$
Work Step by Step
We solve:
$\displaystyle \frac{1}{2}(x-\frac{1}{3})=\frac{3}{4}-\frac{x}{6}
$
$\displaystyle \frac{12}{2}(x-\frac{1}{3})=(\frac{3}{4}-\frac{x}{6})(12)$
$\displaystyle 6(x-\frac{1}{3})=(\frac{3}{4}-\frac{x}{6})(12)$
$6x-2=9-2x$
$6x+2x=9+2$
$8x=11$
$x=\frac{11}{8}$
