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4.5.1 – Solving Absolute Value Inequalities • We’ve now addressed how to solve absolute value equations • We can extend absolute value to inequalities • Remember, the absolute value equation y = |x| is asking for the distance a number x is from zero (left or right) Inequalities • An absolute value inequality is asking for the values that will either be between certain numbers, or outside those numbers • Two cases we will have to consider Case 1 • When given the absolute value inequality |ax + b| > c OR |ax + b| ≥ c, we will setup 2 inequalities to solve • 1) ax + b > c (or ≥) • OR • 2) ax + b < -c (or ≤) • Want to go further away on the distance • Example. Solve the absolute value inequality |x + 4| > 9 • Two inequalities? • Example. Solve the absolute value inequality |2x – 5| ≥ 13 • Two inequalities? Case 2 • The second case will involve staying between two values • When given the absolute value inequality |ax + b| < c or |ax + b| ≤ c, we will set up the following inequality; • -c < ax + b < c • -c ≤ ax + b ≤ c • Example. Solve the absolute value inequality |x + 8| < 10 • Inequality? • Example. Solve the absolute value inequality |-4 + 3x| ≤ 14 • Inequality? Application • Example. The absolute value inequality |t – 98.4| ≤ 0.6 is a model for normal body temperatures of humans at time t. Find the maximum and minimum the internal temperature of a body should be. • Assignment • Pg. 201 • 5-10, 21-29 odd, 34-38, 46, 48