mac1147_lecture9_1_c

# Mac1147_lecture9_1_c - L9 Solving Inequalities Inequalities Involving Absolute Value Graphs 1 Open Intervals x>a a< x

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81 L9 Solving Inequalities Inequalities Involving Absolute Value 1. Open Intervals Graphs Interval Notation x a > axb << x b < 2. Half-open Intervals x a x b ≤< 3. Closed Intervals ≤≤ 4. All real numbers ( ) \ x −∞ < < +∞

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82 Properties of Inequalities : 1. Transitive Property If ab < and bc < , then 2. Addition of Inequalities If < and cd < , then 3. Addition of a Constant c If < , then 4. Multiplying by a Constant c If < and 0 c > , then If < and 0 c < , then Note : When multiplying or dividing both sides by a negative number, reverse the direction of the inequality.
83 5. Reciprocal Properties of Inequality (1) If 0 a > , then 1 0 a > (2) If 0 a < , then 1 0 a < (3) If 0 ab << , then 11 0 >> Proof of (3): Example : Solve the inequalities, graph the solution sets, and give the final answers in interval notation. 28 3 x +< 56 3 x x −≤

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84 Example : Solve the inequalities using the Reciprocal Properties. 1 (3 8) 0 x −< 45 0 6 x <<
85 Solving Combined Inequalities : Example : 8 1 3( 2) 13 x −≤− − < 3 4( 2 ) 5 2 x −≤

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86 Inequalities Involving Absolute Value Recall: x
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## This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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Mac1147_lecture9_1_c - L9 Solving Inequalities Inequalities Involving Absolute Value Graphs 1 Open Intervals x>a a< x

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