I have IP, that I first solved the LP-relaxation and obtained an optimum that is not a whole number. In the optimal table, I selected the following equation
$$ x_2 + 0.25x_3 + 0.25 x_4 = 2.5 $$
where $ x_3, x_4 geq 0 $ they are varaibles loose and $ x_2 geq 0 $. I want to generate a cut of this. The technique I learn is to separate integers on one side of the equation and rational on the other. So, we have
$$ x_2 + x_3 – 0.75 x_3 + x_4 – 0.75 x_4 = 3 – 0.5 $$
$$ x_2 + x_3 + x_4 – 3 = 0.75 x_3 + 0.75 x_4 – 0.5 $$
Now this is where I get stuck, how can I know if RHS is $ geq 0 $ or $ leq 0 $. As far as I can tell, $ x_2 + x_3 + x_4 -3 $ We do not know if it is positive or negative.