Question 984772

1.  The domain of the function   {{{x/abs(x)}}}  is the set of all real numbers except of  x=0. 


2. &nbsp;If x > 0, &nbsp;then &nbsp;{{{x/abs(x)}}} = {{{x/x}}} = 1, &nbsp;and the given inequality takes the form &nbsp;&nbsp;1 < x, &nbsp;&nbsp;i.e. &nbsp;x > 1.


3. &nbsp;If x < 0, &nbsp;then &nbsp;{{{x/abs(x)}}} = {{{x/(-x)}}} = -1, &nbsp;and the given inequality takes the form &nbsp;&nbsp;-1 < x, &nbsp;&nbsp;i.e. &nbsp;x > -1.


<B>Answer</B>. &nbsp;The solution of the given inequality is the union of two sets of real numbers: &nbsp;&nbsp;1) x > 1 &nbsp;&nbsp;and &nbsp;&nbsp;2) -1 < x < 0.