Solve the following

$\frac{2 x+7}{5}-\frac{3 x+11}{2}=\frac{2 x+8}{3}-5$

$\Rightarrow \frac{2 x+7}{5}-\frac{3 x+11}{2}=\frac{2 x+8-15}{3} \quad($ L.C.M. of 3 and 1 is 3$)$

$\Rightarrow 30\left(\frac{2 x+7}{5}\right)-30\left(\frac{3 x+11}{2}\right)=30\left(\frac{2 x+8-15}{3}\right) \quad$ (multiplyin $g$ throughout by 30, which is the L. C.M. of 5,2 and 3$)$

$\Rightarrow 6(2 x+7)-15(3 x+11)=10(2 x+8-15)$

$\Rightarrow 12 x+42-45 x-165=20 x-70$

$\Rightarrow 12 x-45 x+42-165=$$20 x-70$

$\Rightarrow-33 x-123=20 x-70$

$\Rightarrow-33 x-20 x=123-70$

$\Rightarrow-53 x=53$

$\Rightarrow x=\frac{53}{-53}$

$\Rightarrow x=-1$

$\therefore x=-1$