Solve the following

$5 x-\frac{1}{3}(x+1)=6\left(x+\frac{1}{30}\right)$

$\Rightarrow 5 x-\frac{1(x+1)}{3}=6\left(\frac{30 x+1}{30}\right) \quad($ L.C.M. of 1 and 30 is 30$)$

$\Rightarrow 5 x-\frac{(x+1)}{3}=\frac{30 x+1}{5}$

$\Rightarrow \frac{15 x-x-1}{3}=\frac{30 x+1}{5} \quad$ (L.C.M. of 1 and 3 is 3$)$

$\Rightarrow \frac{14 x-1}{3}=\frac{30 x+1}{5}$

$\Rightarrow 5(14 x-1)=3(30 x+1) \quad$ (by cross multiplication)

$\Rightarrow 70 x-5=90 x+3$

$\Rightarrow 70 x-90 x=3+5$

$\Rightarrow-20 x=8$

$\Rightarrow x=\frac{8}{-20}=\frac{-2}{5}$

$\therefore x=-\frac{2}{5}$