Question

Solve each of the following system of equations in R.

5. 3x − 6 > 0, 2x − 5 > 0

Answer 1

$$\begin{gathered} 3x-6>0 \\ \Rightarrow 3x>6 \\ \Rightarrow x>2 \\ \Rightarrow x\in \left(2,\infty \right)...\left(\mathrm{i}\right) \\ \mathrm{Also},2x-5>0 \\ \Rightarrow 2x>5 \\ \Rightarrow x>\frac{5}{2} \\ \Rightarrow x\in \left(\frac{5}{2},\infty \right)...\left(\mathrm{ii}\right) \\ \text{S}\mathrm{olution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right). \\ \left(2,\infty \right)\cap \left(\frac{5}{2},\infty \right)=\left(\frac{5}{2},\infty \right) \\ \mathrm{Thus},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\left(\frac{5}{2},\infty \right). \end{gathered}$$