Question

Solve the inequality for real $x$.

$\frac{x}{3}>\frac{x}{2}+1$

Answer 1

Given, $\frac{x}{3}>\frac{x}{2}+1$

$\Rightarrow \frac{x}{3}-\frac{x}{2}>1$

$\Rightarrow \frac{2x-3x}{6}>1$

$\Rightarrow \frac{-x}{6}>1$

$\Rightarrow x<-6$

$\Rightarrow x\in (-\infty ,-6)$