Question 926070
What is a "distance function"?
Whatever, the written equation seems wrong, otherwise it would simply mean |0|<2, which would be a correct statement but not likely what you were really given.



{{{abs(x/(x-1))<2}}},
two critical values are 0 and 1.  Check the three intervals which these two values create.


{{{x<0,}}}
{{{abs(-2/(-2-1))=abs(2/3)=2/3<2}}}, TRUE.


{{{0<x<1}}}
{{{abs(0.5/(0.5-1))=abs(0.5/(-0.5))=1<2}}}, TRUE.


{{{1<x}}}
{{{abs(3/(3-1))=abs(3/2)=3/2<2}}}, TRUE.


The given inequality seems to be true for all x values  BUT {{{highlight(x<>1)}}}.