Inequalities & RegionsOCR 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]

For example

x

yx > 2 X=2

When dealing with ONE inequality,we SHADE IN the REQUIRED REGION

For example

x

yx < -2 X=-2

For example

x

yy < -1

y=-1

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

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

Drawing InequalitiesBack to Stage 7

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

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

Exam QuestionAn example

y = 3

x = 4x + y = 4y < 3

x < 4

x + y > 4

(3,2)

2 < 3 ?

3 + 2 > 4 ?

3 < 4 ?