Question

$\frac{x+4}{x-3}<2$ is satisfied when $x$ satisfies

• A. $\left(-\infty ,3\right)\cup \left(10,\infty \right)$
• B. $(3,10)$
• C. $\left(-\infty ,3\right)\cup [10,\infty )$
• D. None of these

Answer 1

Answer: (A)

We have, $\frac{x+4}{x-3}<2$ or $\frac{x+4}{x-3}-2<0$
or $\frac{-x+10}{x-3}<0$ or $\frac{x-10}{x-3}>0$
$\Rightarrow$ $\{x-10>0$ and $x-3>0\}$ or $\{x-10<0$ and $x-3<0\}$
$\Rightarrow \{x>10$ and $x>3\}$ or $\{x<10$ and $x<3\}$
$\Rightarrow x\in \left(-\infty ,3\right)\cup \left(10,\infty \right)$