year 8 maths

1B
Substitution and equivalence
11
Example 3 Substituting values
Substitute x = 3 and y = 6 to evaluate the following expressions.
a 5x b 5x 2 + 2y + x
SOLUTION
a 5x = 5(3)
= 15
b 5x 2 + 2y + x = 5(3) 2 + 2(6) + (3)
= 5(9) + 12 + 3
= 45 + 12 + 3
= 60
EXPLANATION
Remember that 5(3) is another way of writing
5 × 3 .
Replace all the pronumerals by their values
and remember the order in which to evaluate
(multiplication before addition).
Example 4 Deciding if expressions are equivalent
a Are x − 3 and 3 − x equivalent expressions?
b Are a + b and b + 2a − a equivalent expressions?
SOLUTION
EXPLANATION
a No The two expressions are equal if x = 3
(both equal zero).
But if x = 7 then x − 3 = 4 and 3 − x = −4 .
Because they are not equal for every single value
of x , they are not equivalent.
b Yes
Regardless of the values of a and b substituted,
the two expressions are equal. It is not possible
to check every single number but we can check a
few to be reasonably sure they seem equivalent.
For instance, if a = 3 and b = 5 , then a + b = 8
and b + 2a − a = 8 .
If a = 17 and b = −2 , then a + b = 15 and
b + 2a − a = 15 .
Exercise 1B
UNDERSTANDING AND FLUENCY
1–4, 5–6(½), 9(½), 11 4, 5–9(½), 10
6–9(½), 10
1 What number is obtained when x = 5 is substituted into the expression 3 × x ?
2 What is the result of evaluating 20 − b if b is equal to 12 ?
3 What is the value of a + 2b if a and b both equal 10 ?
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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