Inequalities & Regions

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# Inequalities & Regions - PowerPoint PPT Presentation

Inequalities & Regions. OCR Module 8. An inequality?. An INEQUALITY shows a relationship between two variables, usually x & y Examples y > 2x + 1 y < x – 3 3x + 4y = 12. What are you required to do?. Read a graph and write down the inequalities that contain a region

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### Inequalities & Regions

OCR Module 8

An inequality?
• An INEQUALITY shows a relationship between two variables, usually x & y
• Examples
• y > 2x + 1
• y < x – 3
• 3x + 4y = 12
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]

y

x

For example

X=2

x > 2

When dealing with ONE inequality,

we SHADE IN the REQUIRED REGION

y

x

For example

X=-2

x < -2

y

x

For example

y < -1

y=-1

y

(1,2)

x

For example

y= 2x+1

y < 2x +1

Which side

Pick a point

NOT on line

Is 2 < 2 x 1 + 1 ?

YES

(1,2) lies in the required region

y

(2,1)

x

For example

y= 3x-2

y > 3x - 2

Which side

Pick a point

NOT on line

Is 1 > 3 x 2 - 2 ?

NO

(2,1) does NOT lie in the required region

### Drawing Inequalities

Back to Stage 7

y

(2,1)

x

How to draw graph of equation

y = 3x + 2

Region for

y > 3x + 2

Is 1 > 3 x 2 + 2 ?

NO

(2,1) does NOT lie in the required region

y

(3,2)

x

How to draw graph of equation

4y + 3x = 12

Region for

4y + 3x > 12

Is 4 x 2 + 3 x 3 > 12 ?

YES

(3,2) DOES lie in the required region

An example

(3,2)

2 < 3 ?

y < 3

x + y = 4

x = 4

3 < 4 ?

y = 3

x < 4

3 + 2 > 4 ?

x + y > 4