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2.4 & 2.5 Absolute Value Inequalities and Equations Learning Goals • Interpret complicated expressions by viewing one or more of their parts as a single entity • Create equations and inequalities in one variable and use them to solve problems absolute value: distance from zero on a number line Ex 1 15 3x 6 Ex 2 2 x9 37 extraneous solution: a solution to a transformed equation but not the original equation Ex 3 5x 2 7x 14 Ex 4 3x 4 4x 1 Ex 5 x x 1 Absolute Value Inequalities a b b a b x 5 distance within 5 units in both directions a b a b or a b x 5 distance outside 5 units in both directions Ex 6 3x 4 8 Ex 7 5x 10 15 Ex 8 2 x 1 5 3 Ex 9 x 5 2 Ex 10 x 5 2 Write each compound inequality as an absolute value inequality. Ex 11 12 m 20 Ex 12 x 1 or x 4 Absolute Value Statements symbols definition distance from x to 0 is a units distance from x to 0 is less than a units distance from x to 0 is greater than a units graph With a partner, graph each solution x 5 and x 6 x 6 or x 5 x5 x