6.6 Solving Absolute Value Inequalities

Absolute Value Inequalities Less than / less than or equal to: If |ax + b | < c where c > 0 then (conjunction) -c < ax + b < c Greater than / greater than or equal to: If | ax + b | > c where c > 0 then (disjunction) ax + b < -c OR ax + b > c Note: With the original inequality, c must be positive because absolute value is distance from 0

I. Solve and graph 1) |x | ≤ 8 2) |x + 3 | > 5

I. Solve and graph cont. 3) 3|5m - 6 | - 8 ≤ 13

I. Solve and graph cont. 4) 2|(1/4)v - 5 | + 4 ≥ 14

II. Translate the sentence into an inequality, solve, and graph 5) Three more than the absolute deviation of -4x from 7 is greater than 10.

III. Tell whether the statements are true or false III. Tell whether the statements are true or false. If false, give a counterexample. If a is a solution of |x + 3 | ≤ 8 then a is also a solution to x + 3 ≥ - 8

III. Tell whether the statements are true or false III. Tell whether the statements are true or false. If false, give a counterexample. If a is a solution of |x + 3 | ≥ 8 then a is also a solution to x + 3 ≤ - 8

IV. Story Problem A company considers people to be full time (without overtime pay) to be 40 hours per week with an absolute deviation of at most 8 hours. The hours worked by employees are: Amy 20, Vince 42, Carl 68, Jo 35, and Janelle 46

IV. Story Problem a) Make a table that shows the absolute deviation of each employee from full time hours (without overtime).

IV. Story Problem b) Write and solve an inequality to find hours allowed. Which people would be considered “full time” (without overtime)?