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Published byLeslie Golden Modified over 8 years ago

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1.6 Absolute Value Equations and Inequalities

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Solving an Absolute Value Equation What is the solution of | 2x – 1 | = 5? Graph the solution. | 2x – 1 | = 5 2x – 1 = 5OR2x – 1 = -5 2x = 6 2x = -4 x = 3OR x = -2

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Solving a Multi-Step Absolute Value Equation What is the solution of 3| x + 2 | - 1 = 8? Graph the solution. 3| x + 2 | - 1 = 8 3 | x + 2 | = 9 | x + 2 | = 3 x + 2 = 3ORx + 2 = -3 x = 1 x = -5

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Checking for Extraneous Solutions What is the solution of | 3x + 2 | = 4x + 5? Graph the solution. | 3x + 2 | = 4x + 5 3x + 2 = 4x + 5 OR 3x + 2 = -(4x + 5) 3x = 4x + 3 3x + 2 = -4x - 5 -x = 3 7x = -7 x = -3 x = -1 Since x = -3 does not satisfy the original equation, -3 is an extraneous solution. The only solution to the equation is x = -1.

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Solving the Absolute Value Inequality | A | < b What is the solution of | 2x – 1 | < 5? Graph the solution. | 2x – 1 | < 5 -5 < 2x – 1 < 5 -4 < 2x < 6 -2 < x < 3

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Solving the Absolute Value Inequality | A | ≥ b What is the solution of | 2x + 4 | ≥ 6? Graph the solution. | 2x + 4 | ≥ 6 2x + 4 ≤ -6OR2x + 4 ≥ 6 2x ≤ -10 2x ≥ 2 x ≤ -5ORx ≥ 1

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More Practice!!!!! Homework – Textbook p. 46 #10 – 36.

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