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]
x>2
y
X=2
For example
x
When dealing with ONE inequality,
we SHADE IN the REQUIRED REGION
x < -2
X=-2 y
For example
x
y
y < -1
For example
x
y=-1
y < 2x +1
For example
Which side
is shaded?
y
y= 2x+1
(1,2)
Pick a point
NOT on line
x
Is 2 < 2 x 1 + 1 ?
YES
(1,2) lies in the required region
y > 3x - 2
y
y= 3x-2
For example
Which side
is shaded?
(2,1)
Pick a point
NOT on line
Is 1 > 3 x 2 - 2 ?
x
NO
(2,1) does NOT lie in the required region
Drawing Inequalities
Back to Stage 7
How to draw graph of equation
y = 3x + 2
y
Shade IN the
Region for
y > 3x + 2
Is 1 > 3 x 2 + 2 ?
(2,1)
NO
(2,1) does NOT lie in the required region
x
How to draw graph of equation
4y + 3x = 12
Shade IN the
Region for
4y + 3x > 12
y
(3,2)
x
Is 4 x 2 + 3 x 3 > 12 ?
YES (3,2) DOES lie in the required region
Exam Question
An example
2<3?
y<3
3<4?
x<4
3+2>4?
x+y>4
x+y=4
x=4
y=3
(3,2)