Inequalities

1. Solving inequalities • Example • Solve the inequality Inequalities Example Solve the inequality

2. Example Solve each of the following inequalities (i) (ii)

3. Representing inequalities on a set of axes • Example • Draw graphs to represent the following inequalities • a) • b) • c) • d) • e)

4. Example Draw a graph and shade the area which represents the set of points that satisfy each of the following inequalities

5. Example Draw the graph and shade the region which represents

6. Forming inequalities • Example • n passengers are sitting on a 56 seated bus. • Example • If Jay receives £ x per week in pocket money, but is never given more than £ 5. • Example • In the school library there are both fiction and non-fiction books. If there are no more than 10 000 books in the library.

7. Linear Programming • Example • A boy decides to buy w white rabbits and b black ones. • Write the following statements as inequalities. • He wants at least two black ones. • He wants at least one white one • His father says he can have no more than 4.

8. Example • A small holder keeps s sheep and p pigs. Make each of these conditions into an inequality • He has housing for only eight animals • He must have at least two pigs to keep each other company • He must have at least three sheep to keep the grass short • His wife insists the sheep outnumber the pigs

9. Example • A man is supplying electrical power to his garage using metres of standard gauge wire and metres of heavy gauge wire. He will need at least two metres of heavy gauge wire. The length of heavy gauge is no more than the length of standard gauge. The total length of wire is no more than 8 metres. • Write three inequalities from the above information and indicate your answers on a diagram. • One metre of standard gauge wire costs £1.50 and one metre of heavy gauge wire costs £2.00. Find the minimum cost of the wire which is needed and say how much of each type of wire should then be bought.