SOLUTION: graph inequality 2x<3y+6

Plot the graph of the equation formed by replacing the < by =

 

Get some points:

 x |  y
 0 | -2
 3 |  0
 6 |  2
-3 | -4

Draw the line dotted since the inequality is < and not <



One side of that dotted line will be shaded, because all the solutions are on
one side of that line and none are on the other side.

Choose a test point which is not on that line, substitute it in original
inequality to find out whether it is a solution or not.  If it is a solution,
then shade the side the test point is on. (That's because if one point on that
side is a solution then they all are.)  If it is not a solution, then shade
the other side of the line.

Let's arbitrarily choose (0,0,) as a test point.  Substitute x=0 and y=0 in
the original inequality:






That is true so the test point (0,0) is a solution, so we shade
the side of the line which the point (0,0) is on.  I can't shade on
here, but you can on your paper.  Shade the whole upper (left) side 
of the dotted line.  (The line was dotted to show that none of the
solutions lie on the line itself.)



Edwin