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Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman

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Solving an Absolute Value Equation |x + 5| = 4 x + 5 = 4 x + 5 = -4

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Solve each x + 5 = 4 x + 5 = -4 -5 -5 -5 -5 x = -1 x = -9

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|3x + 1| + 8 = 10 |3x + 1| = 2 3x + 1 = 2 3x + 1 = -2 -1 -1 -1 -1 3x = 1 3x = -3 3 3 3 3 x = 1/3 x = -1

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Solving an Absolute Value Inequality |x + 5| < 4 x + 5 -4

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Solving an Absolute Value Inequality |x + 3| < 7 x + 3 -7

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Solving an Absolute Value Inequality |x -2| > 8 x - 3 > 8 x - 3 < -8

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Solving an Absolute Value Inequality |x + 3| > 8 x + 3 > 8 x + 3 < -8

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Solving an Absolute Value Inequality If you are solving a “less than” or “less than or equal to” absolute value inequality, the graph of your solution will look like an “and” inequality graph.

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Solving an Absolute Value Inequality If you are solving a “greater than” or “greater than or equal to” absolute value inequality, the graph of your solution will look like an “or” inequality graph.

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Solve |2x – 5| < 4 2x – 5 -4 +5 +5 +5 +5 2x 1 2 2 2 2 x 1/2

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Solve |-2x – 4| > 3 -2x – 4 > 3 -2x – 4 < -3 +4 +4 +4 +4 -2x > 7 -2x < 1 -2 -2 -2 -2 x -1/2

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Try these on your own! 1.3|4x + 1| = 10 2.|5x| + 1 > 16 3.|x – 11| < 21 4.2|-2x – 7| = 20

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That’s all for the day! Thanks for working hard! I’ll see you next time!

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