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Published byBonnie Norton Modified over 9 years ago

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Objectives: Graph the solution sets of compound inequalities. Solve compound inequalities. Standards Addressed: 2.8.8.C: Create and interpret inequalities that model problem situations. 2.8.8.E: Select and use a strategy to solve an inequality and check the solution.

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F > 6 and F < 10 6 < F < 10

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Notice that in Example 1a. that c > 1 AND c 6 AND x < 10. A compound inequality involving AND has a solution region that represents an intersection, or overlapping, of the solution regions for the separate parts of the inequality. These two examples of compound inequalities are called a conjunction.

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A 15,000

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C 65

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Example 2 a and b illustrates the other type of compound inequality, a disjunction. A compound inequality involving OR has solution regions that are the union, or the total, of the solution regions of the separate parts of the inequality.

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A. No solution !! B. Y > -3 AND Y < 6 Q 16

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-6 < 2x + 4 -10 < 2x -5 < x AND 2x + 4 < 10 2x < 6 x < 3 -5 < x < 3

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5x < 15 x < 3 OR 3x – 7 > 23 3x > 30 x > 10 X 10

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2x + 1 < 13 2x < 12 x < 6 OR x – 5 > -5 ALL REALS!!!

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7x + 8 < 43 7x < 35 x < 5 OR x – 16 > -13 x > 3 ALL REALS!!

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AND: intersection or no solution OR: union or All Real #s

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