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Lesson 2-4 Absolute value in open sentence Case1:Case1: |x| = a Case2:Case2: |x| < a Case3:Case3: |x| > a Objective:Objective: Solving absolute value inequality

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Absolute Value of a number is… Lesson 2-4 Definition of Absolute value The distance of that number from zero. |-3| Read as The distance of -3 from zero |-3| = 3 |+5| Read as The distance of +5 from zero |+5| = 5 01234567-2-3-4-5-6-7 -3 01234567-2-3-4-5-6-7 5

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Lesson 2-4Case1:Case1: Solve and graph |x| = a |x| = 7 x = 7x = 7x = -7 OR 01234567-2-3-4-5-6-7 7 Graph

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Lesson 2-4ExampleExample Solve and graph|x + 4| = 5 x + 4 = 5x + 4 = -5 OR -4 x = 1x = -9 01234567-2-3-4-5-6-7-8-9 1 Graph

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Lesson 2-4ExampleExample Solve and graph|2x - 3| - 11 = - 4 Before start solving, you MUST ISOLATE the absolute value expression on one side |2x - 3| - 11 = - 4 +11 |2x - 3| = 7 2x - 3 = 72x - 3 = -7 OR +3 2x = 102x = - 4 2 x = 5 2 x = -2 01234567-2-3-4-5-6-7-8-9 -25

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Lesson 2-4Case2:Case2: |x| < a Solve and graph|x| < 6 -6 < x < 6 01234567-2-3-4-5-6-7 6 -6 Graph

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Lesson 2-4ExampleExample Solve and graph|x + 4| 2 -2 x + 4 2 Graph -4 -6 x -2 01234567-2-3-4-5-6-7 -2 -6

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Lesson 2-4ExampleExample Solve and graph|x - 1| -5 < - 4 -1 < x – 1 < 1 +1 0 < x < 2 01234567-2-3-4-5-6-7 2 0 Before start solving, you MUST ISOLATE the absolute value expression on one side |x - 1| -5 < - 4 +5 |x - 1| < 1

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Lesson 2-4Case2:Case2: |x| > a Solve and graph|x| > 2 x > 6x > 6 01234567-2-3-4-5-6-7 6 -6 Graph x < - 6x < - 6 OR

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Lesson 2-4ExampleExample Solve and graph|x – 3| 1 x – 3 1 01234567-2-3-4-5-6-7 4 2 Graph x – 3 - 1 OR +3 x 4 +3 x 2

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Lesson 2-4ExampleExample Solve and graph|x + 3| + 2 > 5 Before start solving, you MUST ISOLATE the absolute value expression on one side |x + 3| + 2 > 5 -2 |x + 3| > 3 x + 3 > 3 01234567-2-3-4-5-6-7 0 -6 x + 3 < - 3 OR -3 x > 0 -3 x < -6

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Absolute-Value Equations and Inequalities

Absolute-Value Equations and Inequalities

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