LESSON 6-3 COMPOUND INEQUALITIES

1. Objective: To solve and graph inequalities containing “and” or “or”. LESSON 6-3COMPOUND INEQUALITIES

2. Real-World Connection • Do you like to swim? • Does your family have a swimming pool? • Determining how to keep the water in a pool chemically balanced is one way this skill is used in real-world situations.

3. Vocabulary • compound inequality – two inequalities joined by the word and or the word or • solutionfor and inequalities – (Intersection) any number that makes both inequalities true • solutionfor or inequalities – (Union) any number that makes either inequality true

4. STEPS for AND problems • Write the compound inequality as two inequalities joined by and. • Solve each inequality. • Simplify and write the solutions as one statement. • Graph the solution.

5. a. All real numbers that are greater than –2 and less than 3. Graph: b. All real numbers that are less than 0or greater than or equal to 2. Graph: Translate the verbal phrase into an inequality. Then graph the inequality. Inequality: – 2 < x < 3 x < 0 or x ≥ 2 Inequality:

6. c. All real numbers that are less than –1or greater than or equal to 4. All real numbers that are greater than orequal To –3and less than 5. d. Inequality: x < –1 or x ≥ 4 Inequality: x ≥ –3andx < 5 = –3 ≤ x < 5

7. Write and graph a real-world inequality: CAMERA CARS A crane sits on top of a camera car and faces toward the front. The crane’s maximum height and minimum height above the ground are shown. Write and graph a compound inequality that describes the possible heights of the crane.

8. Write and graph a real-world inequality: SOLUTION Let hrepresent the height (in feet) of the crane. All possible heights are greater than or equal to 4 feet and less than or equal to 18 feet. So, the inequality is 4 ≤ h ≤ 18.

9. You try… • Solve each inequality and graph the solution. 1) -6 < 3x < 15 2) -3 < 2x-1 < 7

10. You try… 3) 7 < -3a + 1 < 13 • Solution: -4 < n < -2

11. You try… 4) The books were priced between $3.50 and $6.00, inclusive. • Solution: 3.50 < b < 6

12. To solve OR problems, solve each inequality separately. 5) Solve –2x + 7 > 3 or 3x – 4 > 5.

13. You try… 6) Write an inequality that represents all real numbers that are at most –5 or at least 3. Graph your solution.

14. 7) Graph 3 < 2m – 1 < 9 Remember, when written like this, it is an AND problem! 3 < 2m – 1 AND 2m – 1 < 9 Solve each inequality. Graph the intersection of 2 < m and m < 5. - 5 0 5

15. o o -3 -2 -1 Answer Now Which inequalities describe the following graph? • y > -3 or y < -1 • y > -3 and y < -1 • y ≤ -3 or y ≥ -1 • y ≥ -3 and y ≤ -1

16. Answer Now Which is equivalent to-3 < y < 5? • y > -3 or y < 5 • y > -3 and y < 5 • y < -3 or y > 5 • y < -3 and y > 5

17. Answer Now Which is equivalent to x > -5 and x ≤ 1? • -5 < x ≤ 1 • -5 > x ≥ 1 • -5 > x ≤ 1 • -5 < x ≥ 1

18. Summary • Re-write the compound inequality into two problems and solve. • For and problems, combine the solutions into one statement. • For or problems, solve each separately. • Graph.

19. Homework: • Study for quiz Wednesday, 1/15 • Quiz covers chapter 6 sections 1-3

20. Exit Ticket • Explain the difference between “and” vs. “or” compound inequalities. • How do you solve a compound inequality?