year 8 maths

64 Chapter 2 Equations 2
Example 1
Classifying equations as true or false
For each of the following equations, state whether they are true or false.
a 3 + 8 = 15 − 4
b 7 × 3 = 20 + 5
c x + 20 = 3 × x , if x = 10
SOLUTION
EXPLANATION
a True Left-hand side (LHS) is 3 + 8 , which is 11 .
Right-hand side (RHS) is 15 − 4 , which is also 11 .
Since LHS equals RHS, the equation is true.
b False LHS = 7 × 3 = 21
RHS = 20 + 5 = 25
Since LHS and RHS are different, the equation is false.
c True If x = 10 then LHS = 10 + 20 = 30 .
If x = 10 then RHS = 3 × 10 = 30 .
LHS equals RHS, so the equation is true.
Example 2
Stating a solution to an equation
State a solution to each of the following equations.
a 4 + x = 25
b 5y = 45
c 26 = 3z + 5
SOLUTION
EXPLANATION
a x = 21 We need to find a value of x that makes the equation true.
Since 4 + 21 = 25 is a true equation, x = 21 is a solution.
b y = 9 If y = 9 then 5y = 5 × 9 = 45 , so the equation is true.
c z = 7 If z = 7 then 3z + 5 = 3 × 7 + 5
= 21 + 5
= 26
Note: The fact that z is on the right-hand side of the equation
does not change the procedure.
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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