Inequalities

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Inequalities Regions

• OCR Module 8

2
An inequality?

• An INEQUALITY shows a relationship between two
  variables, usually x y
• Examples
• y gt 2x 1
• y lt x 3
• 3x 4y 12

3
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

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For example
X2
x gt 2
When dealing with ONE inequality, we SHADE IN the
REQUIRED REGION
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For example
X-2
x lt -2
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For example
y lt -1
y-1
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For example
y 2x1
y lt 2x 1
Which side is shaded?
Pick a point NOT on line
Is 2 lt 2 x 1 1 ?
YES
(1,2) lies in the required region
8
For example
y 3x-2
y gt 3x - 2
Which side is shaded?
Pick a point NOT on line
Is 1 gt 3 x 2 - 2 ?
NO
(2,1) does NOT lie in the required region
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Drawing Inequalities

• Back to Stage 7

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How to draw graph of equation
y 3x 2
Shade IN the Region for y gt 3x 2
Is 1 gt 3 x 2 2 ?
NO
(2,1) does NOT lie in the required region
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How to draw graph of equation
4y 3x 12
Shade IN the Region for 4y 3x gt 12
Is 4 x 2 3 x 3 gt 12 ?
YES
(3,2) DOES lie in the required region
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Exam Question

• An example

13
2 lt 3 ?
y lt 3
x y 4
x 4
3 lt 4 ?
y 3
x lt 4
3 2 gt 4 ?
x y gt 4