Question

Let x,y, and z be nonzero real numbers. Find all possible values of
x/|x|+y/|y|+z/|z|+xyz/|xyx|.

Answer 1

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?