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messersmith_power_intermediate_algebra_1e_ch4_7_10

Substitute into Substitute into Test Point x 2 2x 3y 3 Solution? (2, 4) 2 2 True 2(2) 3(4) 3 8 3 True Yes (0, 2) 0 2 True 2(0) 3(2) 3 6 3 True Yes (1, 3) 1 2 True 2(1) 3(3) 3 7 3 False No Although we show three separate graphs in Example 4, it is customary to graph everything on the same axes, shading lightly at fi rst, then to heavily shade the region that is the graph of the compound inequality. YOU TRY 3 EXAMPLE 5 YOU TRY 4 Graph the compound inequality y 3x 1 and y 2x 4. Graph y 1 2 x or 2x y 2. Solution Graph each inequality separately. The solution set of the compound inequality will be the union (total) of the shaded regions. x y 5 5 5 5 y x 12 x y 5 2x y 2 5 5 5 12 Any point 12 in the shaded region of the third graph will be a solution to the compound inequality y x or 2x y 2. This means the point must satisfy y 2x y 2 or both. One point in the shaded region is (2, 3). Substitute into Substitute into Test Point y 12 x 2x y 2 Solution? (2, 3) 3 12 (2) 2(2) 3 2 3 1 False 7 2 True Yes Although (2, 3) does not satisfy y 12 x, it does satisfy 2x y 2, so it is a solution of the compound inequality. Choose a point in the region that is not shaded to verify that it does not satisfy either inequality. Graph the compound inequality x 4 or x 3y 3. x y 5 (2, 3) 5 5 12 y x or 2x y 2 5 x or 192 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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