math unit26 solving inequalities
TRANSCRIPT
Unit 26Solving Inequalities
Presentation 1 Inequalities on a Number Line
Presentation 2 Solving Linear Inequalities
Presentation 3 Inequalities Involving Quadratic Terms
Presentation 4 Graphical Approach
Presentation 5 Linear Programming Problems
Unit 2626.1 Inequalities on a Number
Line
Illustrate these inequalities on the number line and list the integer values which they satisfy each one.
(a)
(b)
(c)
-3-4 0-1-2 31 2-5 4 65
-3-4 0-1-2 31 2-5 4 65
-3-4 0-1-2 31 2-5 4 65
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Which integer values of x satisfy all three inequalities? ?
Unit 2626.2 Solving Linear Inequalities
-3-4 0-1-2 31 2-5 4 65
Solve the following inequalities and illustrate each one on the number line
(a)
(b)
(c)
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-3-4 0-1-2 31 2-5 4 65
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-3-4 0-1-2 31 2-5 4 65
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Unit 2626.3 Inequalities Involving
Quadratic Terms
Solve the following inequalities and illustrate each one on the number line.(a)
(b)
(c)
So either both andi.e. and which means that
Or both andi.e. andwhich means that
-3-4 0-1-2 31 2-5 4 65
-3-4 0-1-2 31 2-5 4 65
-3-4 0-1-2 31 2-5 4 65
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Unit 2626.4 Graphical Approach
A In the diagram below, find the three inequalities which define the shaded region
1 2 3 4 5-5 -4 -3 -2 -1 0
5
4
3
2
1
-1
-2
-3
-4
-5
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x
y
B Find the region satisfied by the inequalities
0 1 2 3 4 5 6 7 8 9
8
7
6
5
4
3
2
1
x
y
Unit 2626.5 Linear Programming
Problems
The shaded area in the diagram shows the solution of a set of inequalities in x and y. The variable x represents the number of boys in a cricket club and y represents the number of girls in the club.
(a) State, using arguments based on the graph, whether the cricket club can have as members(i) 10 boys and 5 girls (ii) 6 boys and 6 girlsSolution
(i) No, as point (10, 5) is not in the feasible region(ii) Yes, as point (6, 6) is in the feasible region ?
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0 5 10 15 20
20
15
10
5
x
y
(b) Write down the set of THREE inequalities that define the shaded region
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0 5 10 15 20
20
15
10
5
x
y
(c) A company sells unifroms for the club and makes a profit of $3.00 on a boys uniform and $5.00 on a girls uniform.
(i) Write an expression in x and y that represents the total profit made by the company on the sales of uniforms.
(ii) Calculate the minimum profit the company can make.
Solution
(i) ??(ii) Vertices of feasible region are
Corresponding values of P are
Minimum profit is at (1, 2) of value $13
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0 5 10 15 20
20
15
10
5
x
y