year 8 maths

2I
Inequalities
101
Example 15
Representing inequalities on a number line
Represent the following inequalities on a number line.
a x ≥ 4
b x < 6
c 1 < x ≤ 5
SOLUTION
a x ≥ 4
3
4
5
6
x
EXPLANATION
A circle is placed at 4 and then the arrow points to the
right, towards all numbers greater than 4 .
The circle is filled (closed) because 4 is included in the set.
b x < 6
3
4
5
6
7
x
A circle is placed at 6 and then the arrow points to the
left, towards all numbers less than 6 .
The circle is hollow (open) because 6 is not included in
the set.
c 1 < x ≤ 5
0
1
2
3
4 5 6
x
Circles are placed at 1 and 5 , and a line goes between
them to indicate that all numbers in between are included.
The circle at 1 is open because the inequality is < not ≤ .
Example 16
Using inequalities to describe real-life situations
Describe the following situations as an inequality, using x to stand for the unknown quantity.
a Fatima is shorter than 160 cm .
b Craig is at least as old as Maria, who is 10 .
c Roslyn’s test score is between 40 and 50 inclusive.
SOLUTION
EXPLANATION
a x < 160 Using x to stand for Fatima’s height, x must be
less than 160 .
b x ≥ 10 Craig is at least 10 , so his age is greater than or
equal to 10 .
c 40 ≤ x ≤ 50 x is between 40 and 50 . The word ‘inclusive’ tells
us that 40 and 50 are both included, so ≤ is used
(rather than < if the word ‘exclusive’ is used).
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.