year 8 maths

2J
Solving inequalities
105
Example 17
Solving inequalities
Solve the following inequalities.
a 5x + 2 < 47 b
SOLUTION
a 5x + 2 < 47
−2
−2
5x < 45
÷5 ÷5
x < 9
3 + 4x
9
≥ 3 c 15 − 2x > 1
EXPLANATION
The inequality is solved in the same way as an equation is
solved: 2 is subtracted from each side and then both sides
are divided by 5 . The sign does not change throughout.
b
3 + 4x
≥ 3
9
×9 ×9
3 + 4x ≥ 27
−3
−3
4x ≥ 24
÷4 ÷4
x ≥ 6
The inequality is solved in the same way as an equation is
solved. Both sides are first multiplied by 9 to eliminate 9
from the denominator.
c 15 − 2x > 1
−15
−15
−2x > −14
÷ −2 ÷ −2
x < 7
15 is subtracted from each side.
Both sides are divided by −2 . Because this is a negative
number, the inequality is reversed from > to < .
Exercise 2J
EXTENSION
UNDERSTANDING AND FLUENCY
1–4, 5–7(½) 4, 5–7(½), 8
5–7(½), 8
1 If x = 3 , classify the following inequalities as true or false.
a x + 4 > 2 b 5x ≥ 10
c 10 − x < 5 d 5x + 1 < 16
2 State whether the following choices of x make the inequality 2x + 4 ≥ 10 true or false.
a x = 5 b x = 1
c x = −5 d x = 3
3 a Copy and complete the following.
2x < 8
÷2 ÷2
x < __
b What is the solution to the inequality 2x < 8 ?
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.