Question

Solve each of the following system of equations in R.

16. $\frac{7x-1}{2}<-3,\frac{3x+8}{5}+11<0$

Answer 1

$$\begin{gathered} \frac{7x-1}{2}<-3 \\ \Rightarrow 7x-1<-6 \\ \Rightarrow 7x<-6+1 \\ \Rightarrow x<\frac{-5}{7} \\ \Rightarrow x\in \left(-\infty ,\frac{-5}{7}\right)...\left(\mathrm{i}\right) \\ \mathrm{Also},\frac{3x+8}{5}+11<0 \\ \Rightarrow \frac{3x+8+55}{5}<0 \\ \Rightarrow 3x+63<0 \\ \Rightarrow 3x<-63 \\ \Rightarrow x<-21 \\ \Rightarrow x\in \left(-\infty ,-21\right)...\left(\mathrm{ii}\right) \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{to}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequations}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right). \\ \left(-\infty ,\frac{-5}{7}\right)\cap \left(-\infty -21\right)=\left(-\infty ,-21\right) \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{to}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequations}\mathrm{is}\left(-\infty ,-21\right). \end{gathered}$$