How do you graph the inequalities

5+g<h
6-h>g
g+h>6

on one coordinate plane

To graph the inequality 5+g<h first consider the equality 5+g=h. This is a straight line that divides the plane into two regions, one region where the inequality is true and the other where the inequality is false. To determine which region is which, choose some point in one of the two regions, I am going to choose (0,0) which is below the line. If I substitute (0,0) into the inequality 5+g<h I get the false statement that 5<0. Thus the region below the line is the region where the inequality is false so the region above the line is the region where the inequality is true.
To graph the inequality I would shade this region in some manner, here I have shaded it green.	Graph of the inequality 5+g<h.
Similarly, for the second and third inequalies, consider the equalities, which turn out to be the same line. This time the point (0,0) satisfies the second inequality and not the third.	Graph of the inequality 6-h>g Graph of the inequality g+h>6.
Here are all three graphs on one coordinate plane. Notice that there are no points that satisfy all there inequalities.	Graph of all three inequalities.