Download - LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”
![Page 1: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/1.jpg)
LESSON 6-3LESSON 6-3COMPOUND COMPOUND INEQUALITIESINEQUALITIESObjective: To solve and graph inequalities containing “and” or “or”.
![Page 2: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/2.jpg)
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.
![Page 3: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/3.jpg)
Vocabulary
compound inequality – two inequalities joined by the word and or the word or
solution for and inequalities – (Intersection) any number that makes both inequalities true
solution for or inequalities – (Union) any number that makes either inequality true
![Page 4: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/4.jpg)
STEPS for AND problems
1. Write the compound inequality as two inequalities joined by and.
2. Solve each inequality.3. Simplify and write the solutions as
one statement.4. Graph the solution.
![Page 5: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/5.jpg)
Translate the verbal phrase into Translate the verbal phrase into an inequality. Then graph the an inequality. Then graph the inequality.inequality.a. All real numbers that are greater than – 2 and less than 3.
Inequality:
Graph:
b.All real numbers that are less than 0 or greater thanor equal to 2.
Inequality:
Graph:
– 2 < x < 3
x < 0 or x ≥ 2
![Page 6: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/6.jpg)
d. All real numbers that are greater than or equal To –3 and less than 5.Inequality:
All real numbers that are less than –1 or greater thanor equal to 4.
c.
Inequality:
= –3 ≤ x < 5 x ≥ –3 and x < 5
x < –1 or x ≥ 4
![Page 7: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/7.jpg)
Write and graph a real-world inequality:
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.
CAMERA CARSCAMERA CARS
![Page 8: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/8.jpg)
Let h represent 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.
SOLUTIONSOLUTION
Write and graph a real-world inequality:
![Page 9: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/9.jpg)
You try…
Solve each inequality and graph the solution.
1) -6 < 3x < 15 2) -3 < 2x-1 < 7
![Page 10: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/10.jpg)
You try…
3) 7 < -3a + 1 < 13
Solution: -4 < n < -2
![Page 11: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/11.jpg)
You try…
4) The books were priced between $3.50 and $6.00, inclusive.
Solution: 3.50 < b < 6
![Page 12: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/12.jpg)
To solve OR problems, solve each inequality separately.5) Solve –2x + 7 > 3 or 3x – 4 > 5.
![Page 13: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/13.jpg)
You try…
6) Write an inequality that represents all real numbers that are at most –5 or at least 3. Graph your solution.
![Page 14: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/14.jpg)
7) Graph 3 < 2m – 1 < 9
Remember, when written like this, it is an AND problem!
3 < 2m – 1 AND 2m – 1 < 9Solve each inequality.
Graph the intersection of 2 < m and m < 5.
0 5-5
![Page 15: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/15.jpg)
Which inequalities describe the following graph?
1. y > -3 or y < -12. y > -3 and y < -13. y ≤ -3 or y ≥ -14. y ≥ -3 and y ≤ -1
-2 -1-3oo
Answer NowAnswer Now
![Page 16: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/16.jpg)
Which is equivalent to-3 < y < 5?
1. y > -3 or y < 52. y > -3 and y < 53. y < -3 or y > 54. y < -3 and y > 5
Answer NowAnswer Now
![Page 17: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/17.jpg)
Which is equivalent to x > -5 and x ≤ 1?
1. -5 < x ≤ 12. -5 > x ≥ 13. -5 > x ≤ 14. -5 < x ≥ 1
Answer NowAnswer Now
![Page 18: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/18.jpg)
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.
![Page 19: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/19.jpg)
Homework:
Study for quiz Wednesday, 1/15
Quiz covers chapter 6 sections 1-3
![Page 20: LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”](https://reader034.vdocument.in/reader034/viewer/2022051516/56649d0b5503460f949deb7c/html5/thumbnails/20.jpg)
Exit Ticket
Explain the difference between “and” vs. “or” compound inequalities.
How do you solve a compound inequality?