Solution:
From the question it is given that \[\frac{x}{3}>\frac{x}{2}+1\]
After rearranging and taking LCM we get,
\[\left( \frac{2x-3x}{6} \right)>1\]
\[-x/6>1\]
\[-x>6\]
\[x<-6\]
The solutions of \[\frac{x}{3}>\frac{x}{2}+1\]are defined by all the real numbers less than \[-6\].
Therefore, the required solution set is \[(-\infty ,-6)\]