question_answer

The inequality \[\frac{2}{x}<3\]is true, when x belongs to

A)  \[\left[ 2/3,\,\infty  \right)\]          

B) \[(-\infty ,\,2/3]\]

C) \[(2/3,\,\infty )\cup (-\infty ,\,0)\]

D) None of these

Correct Answer: C

Solution :

[c] \[\frac{2}{x}<3\Rightarrow \frac{2}{x}-3<0\] \[\Rightarrow \frac{2-3x}{x}<0\] \[\Rightarrow \frac{3x-2}{x}>0\] \[\Rightarrow \frac{3(x-2/3)}{x}>0\] Sign scheme of \[\frac{3(x-2/3)}{x}\]is as follows: \[\Rightarrow x\in (-\infty ,0)\cup (2/3,\infty )\]