Answer
$\displaystyle x=-\frac{27}{13}$
Work Step by Step
We solve:
$\displaystyle \frac{1-3x}{4}=\frac{x+6}{3}+\frac{1}{2}$
$12*(\displaystyle \frac{1-3x}{4})=(\frac{x+6}{3}+\frac{1}{2})(12)$
$\frac{12}{4}(1-3x)=\frac{12}{3}(x+6)+\frac{12}{2}$
$3(1-3x)=4(x+6)+6$
$3-9x=4x+24+6$
$-13x=27$
$x=-\frac{27}{13}$