Solve each of the following system of equations in R.

$\frac{7 x-1}{2}<-3$

$\Rightarrow 7 x-1<-6$

$\Rightarrow 7 x<-6+1$

$\Rightarrow x<\frac{-5}{7}$

$\Rightarrow x \in\left(-\infty, \frac{-5}{7}\right) \quad \ldots$ (i)

$\Rightarrow \frac{3 x+8+55}{5}<0$

$\Rightarrow 3 x+63<0$

$\Rightarrow 3 x<-63$

$\Rightarrow x<-21$

$\Rightarrow x \in(-\infty,-21) \quad \ldots$ (ii)

Hence, the solution to the given set of inequations is the intersection of (i) and (ii).

$\left(-\infty, \frac{-5}{7}\right) \cap(-\infty-21)=(-\infty,-21)$

Hence, the solution to the given set of inequations is $(-\infty,-21)$.