Solve each of the following system of equations in R. 5. 3x − 6 > 0,

$3 x-6>0$

$\Rightarrow 3 x>6$

$\Rightarrow x>2$

$\Rightarrow x \in(2, \infty) \ldots(\mathrm{i})$

Also, $2 x-5>0$

$\Rightarrow 2 x>5$

$\Rightarrow x>\frac{5}{2}$

$\Rightarrow x \in\left(\frac{5}{2}, \infty\right) \ldots$ (ii)

Solution of the given set of inequalities is the intersection of (i) and (ii).

$(2, \infty) \cap\left(\frac{5}{2}, \infty\right)=\left(\frac{5}{2}, \infty\right)$

Thus, the solution of the given set of inequalities is $\left(\frac{5}{2}, \infty\right)$.