# Solve the following

Question:

$\frac{5 x}{2}+\frac{3 x}{4} \geq \frac{39}{4}$

Solution:

$\frac{5 x}{2}+\frac{3 x}{4} \geq \frac{39}{4}$

$\Rightarrow \frac{10 x+3 x}{4} \geq \frac{39}{4}$

$\Rightarrow 10 x+3 x \geq 39$

$\Rightarrow 13 x \geq 39$

$\Rightarrow x \geq \frac{39}{13} \quad$ (Dividing both the sides by 13$)$

$\Rightarrow x \geq 3$

Hence, the solution set of the given inequation is $[3, \infty)$.