Inequality Statements
description
Transcript of Inequality Statements
![Page 1: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/1.jpg)
INEQUALITY STATEMENTS
![Page 2: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/2.jpg)
• “<“ looks like an alligator’s open mouth. The wider part of the opening points toward the larger number.
""""
""
toequalorthangreateristoequalorthanlessis
thangreateristhanlessis
![Page 3: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/3.jpg)
Example……1. 8>2
2. X<3
You cannot list them all because they are infinite but you can show them on a graph.
1. 8 is greater than 2
2. The set of all numbers that make x less than 3
![Page 4: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/4.jpg)
Example……• X<3 would be graphed like this:
![Page 5: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/5.jpg)
• “OPEN Circle” – means the number is NOT part of the solution.
• “CLOSED Circle” = means the number IS part of the solution.
![Page 6: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/6.jpg)
Order of the inequalities……• 8>-4 means the same as -4<8.
• Keep the big mouth pointing toward the same number on either side.
![Page 7: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/7.jpg)
Example…... x 3
![Page 8: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/8.jpg)
Graph: x>2
![Page 9: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/9.jpg)
Graph: x ≤2
![Page 10: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/10.jpg)
Graph: x ≥−3
![Page 11: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/11.jpg)
Graph: x<−5
![Page 12: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/12.jpg)
So what if I took an inequality such as 4 < 8 and added 3 to each side….
![Page 13: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/13.jpg)
So what if I took an inequality such as 4 < 8 and added -5 to each side….
![Page 14: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/14.jpg)
Addition Property of Inequalities• If the same number is added to each side of a true inequality, the resulting inequality is also true.
• 1. If a > b, then a + c > b + c• 2. If a < b, then a + c < b + c
![Page 15: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/15.jpg)
Solve: 𝑥−3>8
![Page 16: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/16.jpg)
Solve: 45≤𝑚−5
![Page 17: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/17.jpg)
Solve: 𝑥+12≤20
![Page 18: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/18.jpg)
Set-Builder Notation• {x | x > 3}
![Page 19: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/19.jpg)
Solve: 27+𝑚>23
![Page 20: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/20.jpg)
Solve: 8−𝑝≤12
![Page 21: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/21.jpg)
Solve: 8 𝑎+4≥7𝑎
![Page 22: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/22.jpg)
Phrases for Inequalities• (<) Less than or fewer than
• (>) Greater than or More than
• ( at most, no more than, less than or equal to
• () at least, no less than, greater than or equal to
![Page 23: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/23.jpg)
Jill has $85 to spend. She went to the store and bought a shirt for $35 and a belt for $18. If she wants to buy a necklace , how much can she spend?
![Page 24: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/24.jpg)
Twice a number increased by 4 is at least 10 more than the number.
![Page 25: Inequality Statements](https://reader036.fdocuments.net/reader036/viewer/2022070422/568163ea550346895dd55d7d/html5/thumbnails/25.jpg)
Homework• Worksheet