year 8 maths

100 Chapter 2 Equations 2
2I Inequalities
EXTENSION
An inequality is like an equation but, instead of indicating that two expressions are equal, it indicates
which of the two has the greater value.
For example, 2 + 4 < 7 , 3 × 5 ≥ 15 and x ≤ 10 are all inequalities. The first two are true, and the last one
could be true or false depending on the value of x .
For instance, the numbers 9.8 , 8.45 , 7 and −120 all make this inequality true.
We could use a number line to represent all the values of x that make x ≤ 10 a true statement.
x
8 9 10 11
Let’s start: Small sums
Two positive whole numbers are chosen: x and y . You are told that x + y ≤ 5 .
• How many possible pairs of numbers make this true? For example, x = 2 and y = 1 is one pair and it
is different from x = 1 and y = 2 .
• If x + y ≤ 10 , how many pairs are possible? Try to find a pattern rather than listing them all.
• If all you know about x and y is that x + y >10, how many pairs of numbers could there be?
Key ideas
■ An inequality is a statement of the form:
• LHS > RHS (greater than). For example: 5 > 2 .
• LHS ≥ RHS (greater than or equal to). For example: 7 ≥ 7 or 10 ≥ 7.
• LHS < RHS (less than). For example: 2 < 10 .
• LHS ≤ RHS (less than or equal to). For example: 5 ≤ 5 or 2 ≤ 5 .
■ Inequalities can be reversed: 3 < x and x > 3 are equivalent.
■ Inequalities can be represented on a number line, using closed circles at the end points if the
value is included, or open circles if it is excluded.
Closed circle
indicates 5 is
included
4
5
x ≥ 5
6
7
x
4
x < 6
5
6
7
Open circle
indicates 6 is
excluded
x
■ A range can be represented as a segment on the number line, using appropriate closed and open
end points.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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