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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 • 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)