Answer
$x=-17$
Work Step by Step
Solving the equation will be easier if there are no fractions involved.
The fractions can be eliminated by multiplying the LCD of $12$ to both sides of the equation:
$12(\frac{1}{4}x-\frac{2}{3})=12(\frac{3}{4}+\frac{1}{3}x)
\\12(\frac{1}{4}x)-12(\frac{2}{3})=12(\frac{3}{4})+12(\frac{1}{3}x)
\\3x-8=9+4x$
Subtract $3x$ and subtract $9$ to both sides of the equation then combine like terms to obtain:
$3x-8-3x-9=9+4x-3x-9
\\-17=x$