Question

Solve each of the following system of equations in R.

9. 3x − 1 ≥ 5, x + 2 > −1

Answer 1

$$\begin{gathered} 3x-1⩾5 \\ \Rightarrow 3x⩾5+1 \\ \Rightarrow x\ge 2 \\ \Rightarrow x\in [2,\infty )...\left(\mathrm{i}\right) \\ \mathrm{Also},x+2>-1 \\ \Rightarrow x>-1-2 \\ \Rightarrow x>-3 \\ \Rightarrow x\in (-3,\infty )...\left(\mathrm{ii}\right) \\ \mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{I}\right)\mathrm{and}\left(\mathrm{ii}\right). \\ [2,\infty )\cap (-3,\infty )=[2,\infty ) \\ \mathrm{Thus},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}[2,\infty ). \end{gathered}$$