mac1147_lecture7_1_b

mac1147_lecture7_1_b - L7 Solving Inequalities;...

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77 L7 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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78 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.
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79 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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80 Example : Solve the inequalities using the Reciprocal Properties. 1 (3 8) 0 x −< 45 0 6 x <<
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81 Solving Combined Inequalities : Example : 8 1 3( 2) 13 x −≤− − < 3 4( 2 ) 5 2 x −≤
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82 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_lecture7_1_b - L7 Solving Inequalities;...

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