Question

Solve each of the following system of equations in R.

3. x − 2 > 0, 3x < 18

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have},x-2>0 \\ \Rightarrow x>2 \\ \Rightarrow x\in \left(2,\infty \right)...\left(\mathrm{i}\right) \\ \mathrm{Also},3x<18 \\ \Rightarrow x<6 \\ \Rightarrow x\in \left(-\infty ,6\right)...\left(\mathrm{ii}\right) \\ \mathrm{Solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{the}\mathrm{inequations}\mathrm{is}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right) \\ \left(2,\infty \right)\cap \left(-\infty ,6\right)=(2,6) \\ \mathrm{Thus},(2,6)\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}. \end{gathered}$$