Question:
Mark the correct alternative in each of the following:
If $\frac{|x-2|}{x-2} \geq 0$, then
(a) $x \in[2, \infty)$
(b) $x \in(2, \infty)$
(c) $x \in(-\infty, 2)$
(d) $x \in(-\infty, 2]$
Solution:
$\frac{|x-2|}{x-2} \geq 0$
$\Rightarrow x-2>0$
$\Rightarrow x>2$
$\Rightarrow x \in(2, \infty)$
Hence, the correct option is (b).