How to enforce a constraint that a decision variable can only take 1 of $k$ integer values? How would you enforce the constraint that $x$, a decision variable, can **only** take values -3, 7, or 19? I think I probably need to introduce a binary variable here but not sure where to start. Thanks.

Let $w,x,y,z \in \mathbb{Z}$ such that:

$x,y,z \in \\{0,1\\}$

$x+y+z=1$

$w=-3x+7y+19z$

Then $w$ will be exactly one out of $-3,7,19$.