Question

Find the solution set of the following inequation :

$\sf{3\:+\:\cfrac{x}{4}\:<\:\cfrac{2x}{3}\:+\:5,\:x\:∈\:Q}$​

Answer 1

$\sf{3\:+\:\dfrac{x}{4}\:<\:\dfrac{2x}{3}\:+\:5,\:x\:∈\:Q}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies\sf{3\:+\:\dfrac{x}{4}\:<\:\dfrac{2x}{3}\:+\:5}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies\sf{\dfrac{x}{4}\:-\:\dfrac{2x}{3}\:<\:5\:-\:3}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies\sf{\dfrac{3x\:-\:8x}{12}\:<\:2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies\sf{\dfrac{-5x}{12}\:<\:2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies\sf{x\:<\:2\:×\:\dfrac{12}{(-5)}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies\sf{x\:>\:\dfrac{-24}{5}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies\sf{x\:>\:=\:-4\:\dfrac{4}{5}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\therefore\sf{\:Solution\:set\:=\:\bigg\{x\:∈\:Q\::\:x\:>\:-4\:\dfrac{4}{5}\bigg\}}$