Question

Solve the following system of equations in R.
$\frac{|x-2|}{x-2}>0$

Answer 1

We have,

$\frac{|x-2|}{x-2}>0...\left(i\right)CaseI:When|x-2|\ge 0x\ge 2\Rightarrow \frac{x-2}{x-2}\ge 0\Rightarrow x-2\ge 0\Rightarrow x\ge 2...\left(ii\right)CaseII:When|x-2|<0x<2\Rightarrow -\frac{(x-2)}{x-2}>0\Rightarrow -(x-2)>0\Rightarrow -x+2>0\Rightarrow -x<-2\Rightarrow x>2...\left(iii\right)\text{Combining (ii) and (iii) we get}(2,\infty )\text{as the solution set.}$