Inequalities

Solving inequalities

Example

Solve the inequality 1742 x

Example

Solve the inequality 4213 xx

Example

Solve each of the following inequalities

(i)

(ii)

162 x

xx 10334

Representing inequalities on a set of axes

Example

Draw graphs to represent the following inequalities

a)

b)

c)

d)

e)

1x

3x2y1y

xy

Example

Draw a graph and shade the area which represents the set of

points that satisfy each of the following inequalities

851,2 xyx

Example

Draw the graph and shade the region which represents 8 yx

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.

Linear Programming

Example

A boy decides to buy w white rabbits and b black ones.

Write the following statements as inequalities.

a) He wants at least two black ones.

b) He wants at least one white one

c) His father says he can have no more than 4.

Example

A small holder keeps s sheep and p pigs. Make each of these

conditions into an inequality

a) He has housing for only eight animals

b) He must have at least two pigs to keep each other company

c) He must have at least three sheep to keep the grass short

d) His wife insists the sheep outnumber the pigs

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.

a) Write three inequalities from the above information and indicate

your answers on a diagram.

b) 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.