Linear Programming Question 93
Question: The inequality $ \frac{2}{x}<3 $ is true, when x belongs to
Options:
A) $ [ 2/3,\infty ) $
B) $ (-\infty ,2/3] $
C) $ (2/3,\infty )\cup (-\infty ,0) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \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 ) $
BETA
