Solve the given inequality

The graphical representation of $x+y \geq 4$ is given by blue line in the figure below.

This lines divides $x-y$ plane into two parts

Select a point (not on the line),which lies on one of the two parts, to determine whether the point satisfies the given inequality or not.

We select the point as $(0,0)$

It is observed that $0+0 \geq 4$ or $0 \geq 4$ which is false.

Therefore, the solution for the given inequality including the points on the line.

This can be represented as follows,