Use the Rearrangement Inequality to show that...
(1) For nonnegative a,b,c, [unparseable or potentially dangerous latex formula]
(2) For positive a,b,c, [unparseable or potentially dangerous latex formula]
(3) [unparseable or potentially dangerous latex formula]
(4) For all a,b,c, [unparseable or potentially dangerous latex formula]
From Engel Ch. 7.