Inequalities and regions 1

Inequalities & Regions

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

You should be able to: • 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

x>2

y

X=2

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

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

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