Question

If $\frac{x-3}{\left|x-3\right|}\ge 0,$ then x belongs to the interval ___________.

Answer 1

$$\begin{gathered} \mathrm{If}\frac{x-3}{\left|x-3\right|}\ge 0 \\ \Rightarrow \left|x-3\right|\ge 0 \\ \mathrm{i}.\mathrm{e}.x-3\ge 0 \\ \mathrm{i}.\mathrm{e}.x\ge 3 \\ \mathrm{i}.\mathrm{e}.x\in [3,\infty ) \end{gathered}$$