If |x-2| x-2 0, then: - Vidyadip

MCQ

If $\frac{|\text{x}-2|}{\text{x}-2}\geq0,$ then:

A
$\text{x}\in[2,\infty)$
✓
$\text{x}\in(2,\infty)$
C
$\text{x}\in(-\infty,2)$
D
$\text{x}\in(-\infty,2]$

✓

Answer

Correct option: B.

$\text{x}\in(2,\infty)$

- For $x-2>0$ (i.e., $x>2$ ):
$|x-2|=x-2, \text { so } \frac{x-2}{x-2}=1 \geq 0 \text { (True) }$
- For $x-2=0$ (i.e., $x=2$ ):
$|x-2|=0$, so $\frac{0}{0}$ is undefined.
- For $x-2<0$ (i.e., $x<2$ ):
$|x-2|=-(x-2)=2-x$, so $\frac{2-x}{x-2}=\frac{-(x-2)}{x-2}=-1 \geq 0$ (False)
$\text{x}\in(2,\infty)$

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