> 1 Multiply both sides by 24 to clear the fraction. 8x + 6y > 24 Divide both sides by 2 to simplify 4x + 3y > 12 First we draw the graph of the boundary line which has equation like the inequality except that we replace the > with = Boundary line's equation is 4x + 3y = 12 Get the intercepts of (3,0) and (0,4) Draw the line dotted, not solid, because the inequality symbol is > and not >, which means that the points on the boundary line are NOT solutions to the inequality. All the solutions to the inequality are on one side or the other of that dotted boundary line. To determine which side of that dotted line we shade, we pick a test point on each side of the line, which can be any arbitrary points as long as they are not on the boundary line. Suppose we pick the test point (4,5) on the upper side of the line and (1,1) on the lower side of the line. We substitute both points in the inequality 4x + 3y > 12 For test pt. (4,5) For test pt. (1,1) 4x + 3y > 12 4x + 3y > 12 4(4) + 3(5) > 12 4(1) + 3(1) > 12 16 + 15 > 12 4 + 3 > 12 31 > 12 7 > 12 TRUE FALSE So we shade the side of the dotted line for which the test point is a solution, which is the side that (4,5) is on, or the upper side, like the green region above the dotted line: Shortcuts: 1. You don't really need to get a test point on but one side of the line, because if it tests TRUE, it is a solution, so you shade that side. If it tests FALSE, it is NOT a solution so the solutions are all on the other side of the line. (The reason I used two test points was to show you what would happen if you picked one on either side). 2. If the line does not go through the origin then you can pick the origin (0,0) as a test point, since 0 is so easy to work with you can probably substitute it in your head. Edwin