year 8 maths

112 Chapter 2 Equations 2
Chapter summary
−5
÷2
Unknown
2x + 5 = 8
2x = 3
3 x =
2
Solution
Equation
−5
÷2 Solving
Solving simple
quadratic equations
If x 2 = c then:
• If c > 0, x = √c or x = − √c
e.g. x 2 = 16 gives x = ±4.
• If c = 0, then x = 0 with one
solution.
• If c < 0, then there are no
solutions for x.
Equivalent equations
stay balanced
5x + 1 = x + 9
−x
−x
−1
4x + 1 = 9
−1
÷4
4x = 8
x = 2
÷4
Equations 2
×3
÷5
Chapter summary
Equations with fractions
5x
3 = 4
5x = 12
x = 12
5
×5
+2
÷3
×3
÷5
3k − 2
= –2
5
3k – 2 = −10
3k = −8
k = −
8
3
9 − 2a −9 3 = 6
−9
×3
− 2a 3 = −3 ×3
−2a = −9
÷ −2 ÷ –2
a = 9 2
×5
+2
÷3
Pronumerals with
negative coefficients
Formulas
rules, relationships
P = 2l + 2b
Equations with brackets
–x = –3
× −1 × −1
x = 3
× −1
−5x = –2
× −1
5x = 2
÷5 x =
2 ÷5
5
subject pronumerals
Expand brackets
Collect like terms
Distributive law
a (b + c)
= ab + ac
5(2x − 3) + 8 = 6x − 19
10x − 15 + 8 = 6x − 19
−6x 10x − 7 = 6x − 19
4x − 7 = −19
+7
4x = −12
÷4
x = −3
−6x
+7
÷4
−3
× −1
× −3
−6
÷ −2
3 − a = 5
−a = 2
a = −2
6 − 2a
= 8
−3
6 − 2a = −24
−2a = −30
a = 15
−3
× −1
× −3
−6
÷ −2
Problem solving
with equations
• Pronumerals: use words to explain
• Rule: starts with word or
pronumeral, has = sign
• Solve: state solution
• Sentence answer with units
An orange costs 5c more than an apple. An
orange and an apple together cost $1.15.
Determine the cost of each.
Cost of apple = x
Cost of orange = x + 5
Total = x + x + 5
2x + 5 = 115
2x = 110
x = 55
Apples cost 55 cents each. Oranges cost
60 cents each.
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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