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 -2 31 2 -5 4 6 5 -3 -4 0 -2 31 2 -5 4 6 5 -3 -4 0 -2 31 2 -5 4 6 5 ? ? ? Which integer values of x satisfy all three inequalities? ?

4. Unit 26 26.2 Solving Linear Inequalities

5. -3 -4 0 -2 31 2 -5 4 6 5 Solve the following inequalities and illustrate each one on the number line (a) (b) (c) ?? -3 -4 0 -2 31 2 -5 4 6 5 ? ? -3 -4 0 -2 31 2 -5 4 6 5 ? ? ? ?

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 bothand i.e. and which means that Or bothand i.e. and which means that -3 -4 0 -2 31 2 -5 4 6 5 -3 -4 0 -2 31 2 -5 4 6 5 -3 -4 0 -2 31 2 -5 4 6 5 ? ? ? ? ? ? ? ? ? ? ?? ?

8. Unit 26 26.4 Graphical Approach

9. A In the diagram below, find the three inequalities which define the shaded region 12345 -5-4-3-2 0 5 4 3 2 1 -2 -3 -4 -5 ? ? ? x y

10. B Find the region satisfied by the inequalities 0123456789 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 ? ? ? ? 05101520 15 10 5 x y

13. (b) Write down the set of THREE inequalities that define the shaded region ? ? ? 05101520 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 ? ? ? ? ? ? ? ?? 05101520 15 10 5 x y