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Let x,y, and z be nonzero real numbers. Find all possible values of

x/|x|+y/|y|+z/|z|+xyz/|xyx|.

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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?

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