mac1140_lecture12_1

# mac1140_lecture12_1 - L12 2.8 Absolute Value Equations...

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93 L12 §2.8 Absolute Value Equations & Inequa l i t ie s Recall : 1. x is the distance on a number line from x to 0. 2. 0 x > if 0 x and 0 x = if and only if 0 x = . 3. xx =− . 4. The algebraic definition: if 0 if 0 x = < . Solving equations of the form x a = Trivial case . Example: 5 x = − 0 a < So lu t ion se t : Nontrivial cases: 1. 0 a = 0 x = 0 x = 2. 0 a > x a = xa = or Important: To use the above results, we must isolate the absolute value.

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94 Example . Solve for x : a) 13 x −= b) 455 x −+ = c) 27 2 5 x + = .
95 Example: Solve for x : 34 2 23 x x = + .

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96 The equation of the form ab = is equivalent to = or = − . Example . Solve the following equation for k : 13 1 kk + =−
97 Solving Absolute Value Inequalities Case 1 : 0 a < Inequality Solution set Examples: 5 x <− x a < 5 x ≤− xa 5 x >− x a > ( ) , −∞+∞ 5 x ≥− x a ( ) , Case 2 : 0 a = Inequality Solution set 0 x < 0 x 0 x = 0 x > { } 0 xx \ 0 x ( ) ,

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98 Recall: x is the distance from x to 0. Case 3 : Inequality Equivalent Inequalities 0 a > x a < axa << x a ≤≤ x a > xa < − or > x a ≤ − or Note : Cases 1 and 2 are based on understanding.

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mac1140_lecture12_1 - L12 2.8 Absolute Value Equations...

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