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]

For example x y x > 2 X=2 When dealing with ONE inequality, we SHADE IN the REQUIRED REGION

For example x y x < -2 X=-2

For example x y y < -1 y=-1

For example x y y < 2x +1 y= 2x+1 Which side is shaded? Pick a point NOT on line (1,2) Is 2 < 2 x ? YES (1,2) lies in the required region

For example x y y > 3x - 2 y= 3x-2 Which side is shaded? Pick a point NOT on line (2,1) Is 1 > 3 x ? NO (2,1) does NOT lie in the required region

Drawing Inequalities Back to Stage 7

How to draw graph of equation x y y = 3x + 2 Shade IN the Region for y > 3x + 2 (2,1) Is 1 > 3 x ? NO (2,1) does NOT lie in the required region

How to draw graph of equation x y 4y + 3x = 12 Shade IN the Region for 4y + 3x > 12 (3,2) Is 4 x x 3 > 12 ? YES (3,2) DOES lie in the required region

Exam Question An example

y = 3 x = 4 x + y = 4 y < 3 x < 4 x + y > 4 (3,2) 2 < 3 ? > 4 ? 3 < 4 ?