Question

Solution of $\left|1+\frac{3}{x}\right|>2$ is

• A. $(0,3]$
• B. $[-1,0)$
• C. $(-1,0)\cup (0,3)$
• D. None of these

Answer 1

Answer: (C)

$\left|1+\frac{3}{x}\right|>2$
Case $I$ : $1+\frac{3}{x}>2\Rightarrow \frac{3}{x}>1$ (Clearly $x>0$)
$\Rightarrow 3>x$ or $x<3$.
Case $II$ : $1+\frac{3}{x}<-2\Rightarrow \frac{3}{x}<-3$ (Clearly $x<0$)
$\Rightarrow 3<-3x\Rightarrow -1<x$ or $x>-1$
Hence, either $0<x<3$ or $-1<x<0$.