A smart thing to would be to make use of the property that difference of any two sides of a triangle is always less than the third side. (which is what the inequality is comparable to). Hence it is true for all .

 

Otherise, substitute and the inequality simplifies to :

 

 

Divide into 3 cases:
Case 1 :



Hence the expression is true in this interval.
Similarly,try out for the other intervals. You will find that it is satisfied.
Case 2:
Case 3:

 

hence .