The given inequality is $ 3x+4y \leq 12$
Consider the equation $3x +4y=12$
The point $(4,0) $ and $(0,3)$ Satisfy the equation
The graphical representation of the line is given below the line divides the x-y plane into two half planes I and II
Select a point not on the line (0,0)
We see that $3(0) +4(0) \leq 12$
or $0 \leq 12$ is true.
Therefore the half plane II is not the solution .
The half plane I containing the point (0,0) is the solution region is the shaded half plane including the points on the line.