Solve the following

$\frac{5 x-4}{6}=4 x+1-\frac{3 x+10}{2}$

$\Rightarrow \frac{5 x-4}{6}=\frac{2(4 x+1)-3 x-10}{2} \quad$ (L.C.M. of 1 and 2 is 2$)$

$\Rightarrow \frac{5 x-4}{6}=\frac{8 x+2-3 x-10}{2}$

$\Rightarrow \frac{5 x-4}{6}=\frac{8 x-3 x+2-10}{2}$

$\Rightarrow \frac{5 x-4}{6}=\frac{5 x-8}{2}$

$\Rightarrow 2(5 x-4)=6(5 x-8)$

$\Rightarrow 10 x-8=30 x-48$

$\Rightarrow 10 x-30 x=-48+8$

$\Rightarrow-20 x=-40$

$\Rightarrow x=\frac{-40}{-20}=2$

$\therefore x=2$