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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

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Presentation Transcript
an inequality
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
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]
for example

y

x

For example

X=2

x > 2

When dealing with ONE inequality,

we SHADE IN the REQUIRED REGION

slide5

y

x

For example

X=-2

x < -2

slide6

y

x

For example

y < -1

y=-1

slide7

y

(1,2)

x

For example

y= 2x+1

y < 2x +1

Which side

is shaded?

Pick a point

NOT on line

Is 2 < 2 x 1 + 1 ?

YES

(1,2) lies in the required region

slide8

y

(2,1)

x

For example

y= 3x-2

y > 3x - 2

Which side

is shaded?

Pick a point

NOT on line

Is 1 > 3 x 2 - 2 ?

NO

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

drawing inequalities

Drawing Inequalities

Back to Stage 7

how to draw graph of equation

y

(2,1)

x

How to draw graph of equation

y = 3x + 2

Shade IN the

Region for

y > 3x + 2

Is 1 > 3 x 2 + 2 ?

NO

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

slide11

y

(3,2)

x

How to draw graph of equation

4y + 3x = 12

Shade IN the

Region for

4y + 3x > 12

Is 4 x 2 + 3 x 3 > 12 ?

YES

(3,2) DOES lie in the required region

exam question

Exam Question

An example

slide13

(3,2)

2 < 3 ?

y < 3

x + y = 4

x = 4

3 < 4 ?

y = 3

x < 4

3 + 2 > 4 ?

x + y > 4