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1. Unit 26
Solving 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

2. Unit 26
26.1 Inequalities on a Number
Line

3. 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
?
?
?
Which integer values of x
satisfy all three inequalities? ?

4. Unit 26
26.2 Solving Linear Inequalities

5. -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)
? ?
-3-4 0-1-2 31 2-5 4 65
? ?
-3-4 0-1-2 31 2-5 4 65
? ? ? ?

6. Unit 26
26.3 Inequalities Involving
Quadratic Terms

7. Solve the following inequalities and illustrate each one on the
number line.
(a)
(b)
(c)
So either both and
i.e. and
which means that
Or both and
i.e. and
which 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
? ?
?
?
? ? ?
?
?
?
? ?
?

8. Unit 26
26.4 Graphical Approach

9.
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
?
?
?
x
y

10.
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

11. Unit 26
26.5 Linear Programming
Problems

12. 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 girls
Solution
(i) No, as point (10, 5) is not in the feasible region
(ii) Yes, as point (6, 6) is in the feasible region
?
?
?
?
0 5 10 15 20
20
15
10
5
x
y

13. (b) Write down the set of THREE inequalities that define the
shaded region
? ? ?
0 5 10 15 20
20
15
10
5
x
y

14. (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
?? ?
?? ?
? ??
0 5 10 15 20
20
15
10
5
x
y