Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two...
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Transcript of Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two...
![Page 1: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/1.jpg)
Inequalities & RegionsOCR Module 8
![Page 2: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/2.jpg)
An inequality?
• An INEQUALITY shows a relationship between two variables, usually x & y
• Examples– y > 2x + 1 – y < x – 3– 3x + 4y = 12
![Page 3: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/3.jpg)
What are you required to
do?
• Read a graph and write down the inequalities that contain a region
• Draw inequalities and indicate the region they describe
• You need to know how to plot straight line graphs [covered in Stage 7]
![Page 4: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/4.jpg)
For example
x
yx > 2 X=2
When dealing with ONE inequality,we SHADE IN the REQUIRED REGION
![Page 5: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/5.jpg)
For example
x
yx < -2 X=-2
![Page 6: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/6.jpg)
For example
x
yy < -1
y=-1
![Page 7: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/7.jpg)
For example
x
yy < 2x +1 y= 2x+1
Which sideis shaded?
Pick a pointNOT on line
(1,2)
Is 2 < 2 x 1 + 1 ?YES (1,2) lies in the required region
![Page 8: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/8.jpg)
For example
x
yy > 3x - 2 y= 3x-2
Which sideis shaded?
Pick a pointNOT on line
(2,1)
Is 1 > 3 x 2 - 2 ?NO
(2,1) does NOT lie in the required region
![Page 9: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/9.jpg)
Drawing InequalitiesBack to Stage 7
![Page 10: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/10.jpg)
How to draw graph of equation
x
yy = 3x + 2Shade IN the Region for y > 3x + 2
(2,1)Is 1 > 3 x 2 + 2 ?NO
(2,1) does NOT lie in the required region
![Page 11: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/11.jpg)
How to draw graph of equation
x
y4y + 3x = 12Shade IN the Region for 4y + 3x > 12 (3,2)
Is 4 x 2 + 3 x 3 > 12 ?YES (3,2) DOES lie in the required region
![Page 12: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/12.jpg)
Exam QuestionAn example
![Page 13: Inequalities & Regions OCR Module 8. An inequality? An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y](https://reader034.fdocuments.us/reader034/viewer/2022052515/5a4d1b657f8b9ab0599af9e3/html5/thumbnails/13.jpg)
y = 3
x = 4x + y = 4y < 3
x < 4
x + y > 4
(3,2)
2 < 3 ?
3 + 2 > 4 ?
3 < 4 ?