Question

If $1+\frac{1}{x}<0$, then $x$ lies in

• A. $(-\infty ,-1)$
• B. $(-1,0)$
• C. $(-1,\infty )$
• D. $(-\infty ,0)$

Answer 1

The correct option is B $(-1,0)$

$1+\frac{1}{x}<0$
$\Rightarrow \frac{x+1}{x}<0$
$\text{I}.$
$x+1<0\text{and}x>0$
$\Rightarrow x<-1,x>0\to \text{not possible}$
$\text{II}.x+1>0$
$\Rightarrow x>-1$ and $x<0$
Taking union of both the cases: $x\in (-1,0)$