Question

If $\frac{|x-3|}{x-3}$ > 0 , then

• A. $x\in (-3,\infty )$
• B. $x\in (3,\infty )$
• C. $x\in (2,\infty )$
• D. $x\in (1,\infty )$
• E. $x\in (-\infty ,3)$

Answer 1

Answer: (B)

We have,
$\frac{|x-3|}{x-3}>0$
Now, $\frac{|x-3|}{x-3}=\{\begin{array}{ll}\frac{x-3}{x-3}=1,& x\ge 3\\ \frac{-(x-3)}{x-3}=-1,& x<3\end{array}$
$\therefore \frac{|x-3|}{x-3}>0$ only holds when $x\in (3,\infty )$