In Linear Programming, we use the “origin side” method to determine which side is the “>” side of the straight line $f(x, y) = 0$.
I know it is NOT necessary true that $f(x, y) > 0$ is always on the “right hand side” of $f(x, y) = 0$. But it seems if we re-write $f(x, y) = 0$ with $((x)) > 0$, that guess is true.
Question:- Is it the case? If it is a yes, then is it a standard method same as the “origin side” and how can we convince others?