Question

Solve the given inequality for real x:

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

Answer 1

Given,

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

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

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

$-x>6$

$x<-6$

Thus, all real numbers $x,$ which are less than $-6,$ are the solutions of the given inequality.

Hence, the solution set of the given inequality is $(-\infty ,-6)$.