Question

Solve each of the following system of equations in R.

1. x + 3 > 0, 2x < 14

Answer 1

$$\begin{gathered} x+3>0 \\ \Rightarrow x>-3 \\ \Rightarrow x\in \left(-3,\infty \right)...\left(\mathrm{i}\right) \\ \mathrm{Also},2x<14 \\ \Rightarrow x<7\left[\mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{sides}\mathrm{by}2\right] \\ \Rightarrow x\in \left(-\infty ,7\right)...\left(\mathrm{ii}\right) \\ \mathrm{Thus},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right). \\ \left(-3,\infty \right)\cap \left(-\infty ,7\right)=\left(-3,7\right) \\ \therefore x\in \left(-3,7\right) \\ \text{Thus, the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\left(-3,7\right). \end{gathered}$$