year 8 maths

2D
Equations with pronumerals on both sides
79
Example 7
Solving equations with pronumerals on both sides
Solve the following equations.
a 7t + 4 = 5t + 10 b 6x + 4 = 22 − 3x c 2u = 7u − 20
SOLUTION
EXPLANATION
a
b
c
−5t
−4
+3x
−4
7t + 4 = 5t + 10
÷2
÷9
−2u
+20
2t + 4 = 10
2t = 6
t = 3
÷2
6x + 4 = 22 − 3x
9x + 4 = 22
÷5
9x = 18
x = 2
÷9
−4
2u = 7u − 20
0 = 5u − 20
20 = 5u
4 = u
∴ u = 4
−4
÷5
−5t
+3x
−2u
+20
Pronumerals are on both sides of the equation, so
subtract 5t from both sides.
Once 5t is subtracted, the usual procedure is
applied for solving equations.
LHS = 7(3) + 4 RHS = 5(3) + 10
= 25 = 25 ✓
Pronumerals are on both sides. To get rid of 3x ,
we add 3x to both sides of the equation.
Alternatively, 6x could have been subtracted from
both sides of the equation to get 4 = 22 − 9x .
LHS = 6(2) + 4 RHS = 22 − 3(2)
= 16 = 16 ✓
Choose to remove 2u by subtracting it.
Note that 2u − 2u is equal to 0 , so the LHS of the
new equation is 0 .
LHS = 2(4) RHS = 7(4) − 20
= 8 = 8 ✓
Exercise 2D
UNDERSTANDING AND FLUENCY
1–3, 4–7(½) 2, 3, 4–7(½)
5–7
1 If x = 3 , are the following equations true or false?
a 5 + 2x = 4x – 1 b 7x = 6x + 5
c 2 + 8x = 12x d 9x − 7 = 3x + 11
2 Fill in the blanks for these equivalent equations.
5x + 3 = 2x + 8
a −2x
−2x
___ = 8
b
9q + 5 = 12q + 21
−9q
−9q
___ = 3q + 12
c
3p + 9 = 5 − 2p
+2p +2p
___ = ___
d
15k + 12 = 13 − 7k
+7k +7k
___ = ___
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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