Download presentation

Presentation is loading. Please wait.

Published byWendy Parrish Modified over 4 years ago

1
6.3 Students will be able to solve compound inequalities.Warm-up Use the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 1. Which numbers are less than or equal to -1 and greater than or equal to -2? 2. Which numbers are greater than 1 or less than -3? 3. Which numbers are less than or equal to -2 and less than or equal to 2? 4. Which numbers are greater than -1 or greater than 3? -2, -1 -5, -4, 2, 3, 4, 5 -5, -4, -3, -2 0, 1, 2, 3, 4, 5

2
6.3 Students will be able to solve compound inequalities. Daily Homework Quiz For use after Lesson 6.2 Solve the inequality. Graph your solution. 1. – 72 < 8p ANSWER p > – 9 2. w – 6 – > – 5 ANSWER W 30 – <

3
6.3 Students will be able to solve compound inequalities. EXAMPLE 1 Write and graph compound inequalities Translate the verbal phrase into an inequality. Then graph the 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 than or equal to 2. Inequality: Graph: – 2 < x < 3 x < 0 or x ≥ 2

4
6.3 Students will be able to solve compound inequalities. 2. All real numbers that are greater than or equal To –3 and less than 5. Inequality: GUIDED PRACTICE Example 1 All real numbers that are less than –1 or greater than or equal to 4. 1. Inequality: = –3 ≤ x < 5 x ≥ –3 and x < 5 x < –1 or x ≥ 4

5
6.3 Students will be able to solve compound inequalities. CAMERA CARS EXAMPLE 2 Write and graph a real-world compound 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.

6
6.3 Students will be able to solve compound inequalities. EXAMPLE 2 Write and graph a real-world compound inequality 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. SOLUTION

7
6.3 Students will be able to solve compound inequalities. SOLUTION Solve Solve a compound inequality with and 2 < x + 5 < 9. Graph your solution. Separate the compound inequality into two inequalities. Then solve each inequality separately. 2 < x + 5 Write two inequalities. 2 – 5 < x + 5 – 5 Subtract 5 from each side. –3 < x Simplify. The compound inequality can be written as – 3 < x < 4. x + 5 < 9 x + 5 – 5 < 9 – 5 x < 4 and

8
6.3 Students will be able to solve compound inequalities. EXAMPLE 3 Solve a compound inequality with and ANSWER The solutions are all real numbers greater than –3 and less than 4. Graph:

9
6.3 Students will be able to solve compound inequalities. SOLUTION GUIDED PRCTICE for Example 2 and 3 An investor buys shares of a stock and will sell them if the change c in value from the purchase price of a share is less than –$3.00 or greater than $4.50. Write and graph a compound inequality that describes the changes in value for which the shares will be sold. 3. Let c represent the change in the value from the purchase price of the shares where all possible changes are less than –$3.00 or greater than $4.50. Investing

10
6.3 Students will be able to solve compound inequalities. for Example 2 and 3 So the inequality is c 4.5. ANSWER

11
6.3 Students will be able to solve compound inequalities. SOLUTION EXAMPLE 3 Solve a compound inequality with and Solve the inequality. Graph your solution. Separate the compound inequality into two inequalities. Then solve each inequality separately. –7 < x – 5 Write two inequalities. –7 + 5 < x –5 + 5 Add 5 to each side. –2 < x Simplify. The compound inequality can be written as – 2 < x < 9. –7 < x – 5 < 4 4. and x – 5 < 4 x – 5 + 5 < 4 + 5 x < 9 and

12
6.3 Students will be able to solve compound inequalities. EXAMPLE 3 ANSWER The solutions are all real numbers greater than –2 and less than 9. for Example 2 and 3 – 6 – 4 – 2 0 2 4 6 8 10 9 Graph:

13
6.3 Students will be able to solve compound inequalities. SOLUTION Solve the inequality. Graph your solution. Separate the compound inequality into two inequalities. Then solve each inequality separately. 10 ≤ 2y + 4 Write two inequalities. 10 – 4 ≤ 2y + 4 – 4 Subtract 4 from each side. Simplify. The compound inequality can be written as 3 ≤ y ≤ 10. 10 ≤ 2y + 4 ≤ 24 5. 6 ≤ 2y 3 ≤ y GUIDED PRACTICE for Example 2 and 3 2y + 4 ≤ 24 2y + 4 – 4 ≤ 24 – 4 2y ≤ 20 y ≤ 10 and

14
6.3 Students will be able to solve compound inequalities. EXAMPLE 3 Solve a compound inequality with and ANSWER The solutions are all real numbers greater than or equal to 3 and less than or equal to 10. 0 2 4 6 8 10 12 Graph: 3

15
6.3 Students will be able to solve compound inequalities. SOLUTION Solve a compound inequality with and Solve the inequality. Graph your solution. Separate the compound inequality into two inequalities. Then solve each inequality separately. –z – 1 < 3 Write two inequalities. –7 + 1< –z – 1 + 1 Add 1 to each side. Simplify. –7< –z – 1 < 3 6. 6 < z –7 < –z – 1 and –z – 1 + 1 < 3 + 1 z > – 4 and The compound inequality can be written as – 4 < z < 6.

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google