Systems of Linear Inequalities with 3 or More Variables

How many of the 8 octants does the plane $x+y+z = 0$ intersect?

Note: There are 8 octants in space: for instance, one of them is $x>0$, $y>0$, $z>0$, which can be thought of as $(+,+,+)$ (all coordinates positive). The other 7 are given by other choices of signs, like $(-,+,-)$ (which means $x,z$ coordinates negative and $y$ coordinate positive).