Question

If $\frac{5}{x-2}>3,$ then

• A. $x\in (2,\frac{11}{3})$
• B. $x\in (0,\frac{11}{3})$
• C. $x\in (-\infty ,\frac{11}{3})$
• D. $x\in (-\infty ,2)\cup (\frac{11}{3},\infty )$

Answer 1

The correct option is A $x\in (2,\frac{11}{3})$

$\frac{5}{x-2}>3\Rightarrow \frac{1}{x-2}>\frac{3}{5}\Rightarrow \frac{3}{5}<\frac{1}{x-2}<\infty$
$\because 0$ is not lying in the interval
$\therefore 0<x-2<\frac{5}{3}\Rightarrow 0+2<x<\frac{5}{3}+2\therefore x\in (2,\frac{11}{3})$