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Published byAnn Preston Modified over 7 years ago

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Solving Inequalities with Absolute Value

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Things we already know about Inequalities!! >, < : on graph =, ≤, ≥, : on graph When dividing or multiplying by a NEGATIVE number, we reverse the inequality symbol!!

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Steps for Solving Inequalities with Absolute Values 1.Make sure Absolute Value is isolated! (Are there numbers not in the absolute value symbol?) **Don’t forget when dividing or multiplying by negative number, reverse inequality symbol** 2.Make 2 Inequalities: 1. One inequality has EXACT inequality = positive answer 2. One inequality has REVERSE inequality = negative answer

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Steps for Solving Inequalities with Absolute Values 3.Solve Inequalities following inequality rules!! **Don’t forget when dividing or multiplying by negative number, reverse inequality symbol** 4.Graph on number line using inequality rules!! >, < : on graph =, ≤, ≥, : on graph

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Let’s Goooooooooooooo!!! 1. |n + 2| < 2 Is the absolute value isolated? Write the 2 related inequalities. Solve each inequality. Graph your solution. n + 2 < 2 n + 2 > -2 n + 2 > -2 - 2 -2 n > -4 n + 2 < 2 -2 -2 n < 0

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2. |-6 + n| > 12 Is the absolute value isolated? Write the 2 related inequalities. Solve each inequality. Graph your solution. - 6 + n > 12 -6 + n < -12 n < -6 +6 + 6 n > 18

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