year 8 maths

2A
Reviewing equations
67
15 a Explain why the equation x + 3 = x has no solutions.
b Explain why the equation x + 2 = 2 + x is true, regardless of the value of x .
c Show that the equation x + 3 = 10 is sometimes true and sometimes false.
d Classify the following equations as always true (A), sometimes true (S) or never true (N).
i x + 2 = 10
ii 5 − q = q
iii 5 + y = y
iv 10 + b = 10
v 2 × b = b + b
vi 3 − c = 10
vii 3 + 2z = 2z + 1
viii 10p = p
ix 2 + b + b = (b + 1) × 2
e Give a new example of another equation that is always true.
16 a The equation p × (p + 2) = 3 has two solutions. State the two solutions.
(Hint: one of them is negative.)
b How many solutions are there for the equation p + (p + 2) = 3 ?
c Try to find an equation that has three solutions.
ENRICHMENT
– –
17, 18
More than one unknown
17 a There are six equations in the square below. Find the values of a , b , c , d and e to make all six
equations true.
a + 12 = 22
× ÷ −
2 × b = c
= = =
d ÷ e = 10
b Find the value of f that makes the equation a × b × e = c × d × f true.
18 For each of the following pairs of equations, find values of c and d that make both equations true.
More than one answer may be possible.
a c + d = 10 and cd = 24
b c − d = 8 and c + d = 14
c c ÷ d = 4 and c + d = 30
d cd = 0 and c − d = 7
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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