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messersmith_power_intermediate_algebra_1e_ch4_7_10

YOU TRY 2 Graph each inequality using the slope-intercept method. a) y 3 4 x 6 b) 5x 2y 4 2 Graph a Compound Linear Inequality in Two Variables Linear inequalities in two variables are called compound linear inequalities if they are connected by the words and or or. The solution set of a compound inequality containing and is the intersection of the solution sets of the inequalities. The solution set of a compound inequality containing or is the union of the solution sets of the inequalities. Procedure Graphing Compound Linear Inequalities in Two Variables 1) Graph each inequality separately on the same axes. Shade lightly. 2) If the inequality contains and, the solution set is the intersection of the shaded regions. Heavily shade this region. 3) If the inequality contains or, the solution set is the union (total) of the shaded regions. Heavily shade this region. EXAMPLE 4 Graph x 2 and 2x 3y 3. Solution To graph x 2, graph the boundary line x 2 as a solid line. The x-values are less than 2 to the left of 2, so shade the region to the left of the line x 2. Graph 2x 3y 3. Use a dotted boundary line. The region shaded blue in the third graph is the intersection of the shaded regions and the solution set of the compound inequality. The part of the line x 2 that is above the line 2x 3y 3 is included in the solution set. x 2 and 2x 3y 3 T x y 5 x 2 5 5 5 x y 5 2x 3y 3 5 5 5 x y 5 2 2 2 5 5 1 5 Any point in the solution set must satisfy both inequalities, and any point not in the solution set will not satisfy both inequalities. We check three test points next. (See the graph.) Notice that the final solution is the set of ordered pairs that lie in the overlapping shaded region. SECTION www.mhhe.com/messersmith 4.4 Linear and Compound Linear Inequalities in Two Variables 191


messersmith_power_intermediate_algebra_1e_ch4_7_10
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