Let x,y, and z be nonzero real numbers. Find all possible values of
x/|x|+y/|y|+z/|z|+xyz/|xyx|.
If x,y,z are all positive, then the sum is
1+1+1+1 = 4
If any are negative, then u/|u| becomes -1, and the total is less.
I guess you can list the possibilities, eh?