1. LESSON 6.1 – SOLVING ABSOLUTE VALUE EQUATIONS AND INEQUALITIES DAY 1

2. WARM UP Suppose you are driving a car. Going too fast is obviously a hazard and might earn a speeding ticket. Going too slow is also a hazard, and can earn a ticket also. A ticket is given when someone is going at least 15 mph different than the rest of the cars. If most of the cars are moving at 65mph, at what speed can you be pulled over? Do we represent this as an inequality or an equation? Explain your reasoning. If your speed is 75, will you be pulled over?

3. SOLUTIONS If most of the cars are moving at 65mph, at what speed can you be pulled over? Do we represent this as an inequality or an equation? Explain your reasoning. If your speed is 75, will you be pulled over?

4. PREVIOUS KNOWLEDGE How many solutions does the problem |x| = 8 have? Why? How do we solve an equation or an inequality? What must you remember about solving inequalities?

5. BACK TO OUR WARM UP The difference from your speed to everyone else’s speed has to be within 15mph in order to avoid a ticket. What speed would cause a ticket? x-65 = -15 +65 +65 x = 50 |x-65| = 15 x-65 = 15 +65 +65 x = 80 You will receive a ticket if you are going 80mph or 50mph

6. WHAT ARE SOME OTHER REAL LIFE EXAMPLES OF ABSOLUTE VALUE SITUATIONS? Body temperature and being at risk Weight for being healthy

7. EXAMPLE 1: It’s common knowledge that a person’s normal body temperature is supposed to be 98.6 degrees. Physicians say that people’s body temperature shouldn’t exceed 0.5 degrees from the norm, or they may be sick. How can we represent this relationship as an absolute value equation, and then solve to know what the minimum and maximum body temperatures are? |t−98.6|=0.5

8. EXAMPLE 2: The water temperature in a certain production process should be 143°F. If the actual temperature differs by 13 degrees from what it should be, then what is the actual temperature?

9. TRY THESE |x-4| = 7|x-24|=6

10. BUT WHAT ABOUT THESE EXAMPLES: Example 3: |3x| = 9 Example 4: |x/2| = 6.

11. BUT WHAT ABOUT THESE EXAMPLES: Example 5: |2x – 2| = 10 Example 6: |2x - 7|- 5 = 4.

12. TRY THESE |2x-4|=1 -2|5-x|=-14

13. 2|5-2x|-15=5

14. CLASSWORK Please choose a partner for this activity. I need: 1 person to go get a ruler from the drawer The other person to come to the front and get a bullseye and a pack of M&M’s/Skittles PLEASE DO NOT EAT THE M&M’S OR SKITTLES Instructions: You and your partner will take turns dropping a M&M or Skittle from arms length down to the bullseye. You will measure how far away the M&M landed from the bulls eye. Record ten different times, then calculate the average distance. Using an absolute value equation, determine how far each of your results were from the average.

15. HOMEWORK Complete attached worksheet on solving absolute value inequalities.

16. SOLVING ABSOLUTE VALUE INEQUALITIES DAY 2

17. WARM UP Consider this: A candy manufacture puts 240 pieces of candy into each bag. The bag can be off by 8 pieces. What is the most and least amount of candy that could be in a bag? Would you represent this as an inequality or an equation? Why?

18. A CANDY MANUFACTURE PUTS 240 PIECES OF C ANDY INTO EACH BAG. THE BAG CAN BE OFF BY 8 PIECES.

19. PREVIOUS KNOWLEDGE How do we solve an absolute value problem, say |3x + 4| = 10 For any absolute value equation, how many solutions will we have?

20. BACK TO OUR WARM UP

21. OTHERS? What are some other instances we could use an absolute value inequality?

22. EXAMPLE 1: An essay contest requires that essay entries consist of 500 words with an absolute deviation of at most 30 words.

23. EXAMPLE 2: A clothing designer is selecting models to walk the runway for her fashion show. The designer prefers models that are no more than 3 inches away from being 5’10”. Since 5’10” is the same as 70”, what would the inequality to determine if a model’s height x is within the preferred height range?

24. TRY THESE

25. BUT WHAT ABOUT

27. TRY THESE

28. 14 – | x − 19 | ≥ 20

29. CLASSWORK Work on attached worksheet

30. HOMEWORK Finish Packet