in trying to solve the following inequality : the following proof went through my mind ,but i am not sure if it is correct:
Assume 1-x<0 ,then the inequality becomes ,if we multiply across : 1/x <0 ,which implies that x<0.
BUT since 1<x ( 1-x<0) we have 1<0 , a contradiction,hence .
BUT since [(1-x)<0 or (1-x)>0] ,and since we have (1-x)>0
Hence the inequality is satisfied for all ,x<1