September 22, 2011 At the end of today, you will be able to: Solve compound inequalities using “and” Solve Absolute value inequalities Warm-up: How much dirt is in a hole that is 1.5ft deep, 2ft width, and a length of 3ft? HW 1.6 Worksheet

Check HW 1.5 Pg. 37 – check odds in back of book. Pg. 44 8) {y| y > 4 or y < -1}, see graph on board 9) {d| -2 < d < 3}, graph on board 27) {p| p ≤ 2 or p ≥ 8}, graph on board 28) {t| 1< t < 3} 29) {x| -2 < x < 4}

General rules for “And” and “Or” Compound Inequalities Shaded in between two numbers Inequality looks like, 3 ≤ x ≤ 8 “Or” Shaded outward Inequality looks like, x < -3 or x > 7 20 -15 -5 5 15 -20 -10 10 20 -15 -5 5 15 -20 -10 10

Lesson 1.6 Absolute Value Inequalities Absolute Value Inequalities is about the distance from 0. |x| < 4 “What values for x is less than 4 steps away from 0?” 20 -15 -5 5 15 -20 -10 10 {x| -4 < x < 4} It’s an “and” inequality because it is shaded in between.

Graph the values for |x| ≥ 4 “What values of x are 4 or more steps away from 0?” {x| x ≤ -4 or x ≥4 } 20 -15 -5 5 15 -20 -10 10 It’s an “or” inequality because it is shaded outward.

Solving Absolute Value Inequalities Use the same steps you used to solve for Absolute Value Equations! Set up 2 equations: each for the positive and negative solutions Flip the inequality for the negative case. Example 1) Solve, then graph |3x -12| ≥ 6 3x – 12 ≥ 6 3x – 12 ≤ -6 x ≥ 6 x ≤ 2 20 -15 -5 5 15 -20 -10 10 Since the graph goes outward, the answer is: {x| x ≤ 2 OR x ≥ 6}

Practice: |4k – 8| < 20 5.|-5y| ≤ 36 6. |x + 8| - 10 > -4

Example 2 Absolute Value Word Problems To prepare for a job interview, Megan researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ by as much as $2450. Write an absolute value inequality to describe this situation. Solve the inequality to find the range of Megan’s starting salary.

1. Hypothermia and hyperthermia are conditions potentially dangerous and occur when a person’s body temperature fluctuates by more than 8° from the normal body temperature of 98.6°F. Write and solve an absolute value inequality to describe body temperatures that are considered potentially dangerous.

2. A company’s guidelines call for each can of soup produced not to vary from its stated volume of 14.5 fluid ounces by more than 0.08 ounces. Write and solve an absolute value inequality to describe acceptable can volumes.

3. To get a chance to win a car, you must guess the number of keys in a jar to within 5 of the actual number. Those who are within this range are given a key to try the ignition of the car. Suppose there are 587 keys in the jar. Write and solve an inequality to determine the number of guesses that will give the contestants a chance to win the car.

4. In 90% of the last 30 years, the rainfall at Seal Beach has varied no more than 6.5 inches from its mean value of 24 inches. Write and solve an absolute value inequality to describe the rainfall in the other 10% of the last 30 years.