Chapter 1 Section 1.7

Yesterday’s Exit Slip -2

Objectives: O To solve compound inequalities using and and or. O To solve inequalities involving absolute value and graph the solutions. Why do we need this? You can use absolute value inequalities to solve problems involving entertainment and education.

Compound Inequalities A compound inequality is an equation with two or more inequalities joined together with either "and" or "or“. AND means intersection -what do the two items have in common? OR means union -if it is in one item, it is in the solution A A B B

Example Graph x < 4 and x ≥ 2 a) Graph x < 4 b) Graph x ≥ 2 c) Combine the graphs d) Where do they intersect? o ● ● o

Example Graph x < 2 or x ≥ 4 a) Graph x < o b) Graph x ≥ ● c) Combine the graphs o ●

Example Solve and Graph: 9 < 3x + 6 < 15 9 < 3x + 6 < 15 9 < 3x + 6 3x + 6 < 15 1 < x x < < x < 3

Solving Absolute Value Inequality Why do you think we need to review compound inequalities before continuing with absolute value inequalities?

Example Solve and Graph: |2x + 4|  12 |2x + 4|  12 2x + 4  122x + 4  -12 2x  8 x  4 2x  -16 x  great OR or

Example Solve and Graph: |x - 3| < 2 |x - 3| < 2 x -3 < 2x – 3 > -2 x < 5 x > less th and and

Writing Absolute Value Inequalities You work in the quality control department of a manufacturing company. The diameter of a drill bit must be between 0.62 inch and 0.63 inch. Write an absolute-value inequality to represent this requirement. How do we solve this?

Solution Let d represent the diameter (in inches) of the drill bit. O Write a compound inequality. O Find the halfway point. O Subtract from each part of the compound inequality. O Rewrite as an absolute-value inequality ≤ d ≤ ≤ d ≤ ≤ d ≤ |d |≤ 0.005

Mid-Exit tickets These were our objectives: O To solve compound inequalities using and and or. O To solve inequalities involving absolute value and graph the solutions. Keep these in mind while answering your questions.