Inequalities
Solving inequalities
Example
Solve the inequality
2 x  4  17
Example
Solve the inequality
3x  1  2 x  4
Example
Solve each of the following inequalities
(i)
x 2  16
(ii) 4x  3  310  x
Representing inequalities on a set of axes
Example
Draw graphs to represent the following inequalities
a)
x 1
b)
x3
c)
y2
d)
y  1
e)
yx
Example
Draw a graph and shade the area which represents the set of
points that satisfy each of the following inequalities
x  2, 1  y  5 x  8
Example
Draw the graph and shade the region which represents
x y 8
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.