Remember (definition/properties of abs. val.) that for , so:
,and now you have an "and" inequality system: both the left AND the right inequalities have to be true, so solve them separately and then take the intersection of the separate solutions. For example:
, and since both the numerator and the denominator are ALWAYS positive (why?)
this inequality is true for all ;
...and now can you see why this is ALWAYS negative?
Interestingly enough, the given inequality is true for all x, imo, and thus I can't understand why they gave you that ...