Question

Mark the correct alternative in each of the following:
If $\frac{\left|x-2\right|}{x-2}$$\ge$0, then
(a) x$\in$[2, $\infty$)
(b) x$\in$(2, $\infty$)
(c) x$\in$($-$$\infty$, 2)
(d) x$\in$($-$$\infty$, 2]

Answer 1

$$\begin{gathered} \frac{\left|x-2\right|}{x-2}\ge 0 \\ \Rightarrow x-2>0 \\ \Rightarrow x>2 \\ \Rightarrow x\in \left(2,\infty \right) \end{gathered}$$

Hence, the correct option is (b).