year 8 maths

2C
Equations with fractions
77
10 To solve an equation with a variable as the denominator we can first multiply both sides by that
variable.
30
x = 10
×x ×x
30 = 10x
÷10 ÷10
3 = x
Use this method to solve the equations.
12
a
x = 2 b −15
= −5
x
1
c
x + 3 = 4 d 4 + 20 x = 14
16
e
x + 1 = 3 f 5 = −10 + 3
x
ENRICHMENT
– –
11, 12
Fractional solutions
11 Solve the following equations. Note that the solutions should be given as fractions.
a
4x + 3
5
8 + 3x
= 12 b = 6
5
10 − 3x
d 2 =
4
c 7 = x 4 + 1 3
12 Recall from Section 1E (Adding and subtracting algebraic fractions) that algebraic fractions can be
combined by finding a common denominator. For example:
2x
3 + 5x
4 = 8x
12 + 15x
12
= 23x
12
Use this simplification to solve the following equations.
2x
a
3 + 5x
4 = 46 b x
5 + x 6 = 22
c 10 = x 2 + x 3
d 4 = x 2 − x 3
e
6x
5 + 2x
3x
= 28 f 4 =
3 7 − x 3
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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