year 8 maths

78 Chapter 2 Equations 2
2D Equations with pronumerals on both sides
So far all the equations we have considered involved a pronumeral either on the left-hand side
(e.g. 2x + 3 = 11 ) or on the right side (e.g. 15 = 10 − 2x) . But how can you solve an equation with
pronumerals on both sides (e.g. 12 + 5x = 16 + 3x )? The idea is to look for an equivalent equation with
pronumerals on just one side.
The equation 12 + 5x = 16 + 3x can be thought of as
balancing scales, as shown on the right.
12
x x
x
16
x x 16
x x
x
Then 3x can be removed from both sides of this equation to get:
12
x x
The resulting equation 12 + 2x = 16 is straightforward to solve.
Let’s start: Moving pronumerals
You are given the equation 11 + 5x = 7 + 3x .
• Can you find an equivalent equation with x just on the left-hand side?
• Can you find an equivalent equation with x just on the right-hand side?
• Try to find an equivalent equation with 9x on the left-hand side.
• Do all of these equations have the same solution? Try to find it.
Key ideas
■ If both sides of an equation have a pronumeral added or subtracted, the new equation will be
equivalent to the original equation.
■ If pronumerals are on both sides of an equation, add or subtract it so that the pronumeral
appears on only one side. For example:
10 + 5a = 13 + 2a 4b + 12 = 89 − 3b
−2a −2a +3b +3b
10 + 3a = 13 7b + 12 = 89
■ Sometimes it is wise to swap the left-hand side and right-hand side.
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.