Question

Solve each of the following system of equations in R.

8. 5x − 1 < 24, 5x + 1 > −24

Answer 1

$$\begin{gathered} 5x-1<24 \\ \Rightarrow 5x<24+1 \\ \Rightarrow x<5 \\ \Rightarrow x\in \left(-\infty ,5\right)...\left(\mathrm{i}\right) \\ \mathrm{Also},5x+1>-24 \\ \Rightarrow 5x>-24-1 \\ \Rightarrow x>-5 \\ \Rightarrow x\in (-5,\infty )...\left(\mathrm{ii}\right) \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right). \\ \left(-\infty ,5\right)\cap \left(-5,\infty \right)=\left(-5,5\right) \\ \mathrm{Thus},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\left(-5,5\right). \end{gathered}$$