Solve the following

Question:

Solve $\frac{|x-2|}{x-2}>0$

Solution:

We have,

$\frac{|x-2|}{x-2}>0$

As, $|x-2|=\left\{\begin{array}{l}x-2, x \geq 2 \\ 2-x, x<2\end{array}\right.$

And $\frac{|x-2|}{x-2}>0$ for $x>2$

So, $x>2$

$\therefore x \in(2, \infty)$