year 8 maths

2E
Equations with brackets
85
3 Rolf is unsure whether 4(x + 3) is equivalent to 4x + 12 or 4x + 3 .
a Fill out the table below.
x 0 1 2
4(x + 3)
4x + 12
4x + 3
b What is the correct expansion of 4(x + 3) ?
4 Simplify the following expressions by collecting like terms.
a 4x + 3x b 7p + 2p + 3 c 8x − 2x + 4
d 2k + 4 + 5k e 3x + 6 − 2x f 7k + 21 − 2k
Example 8a
Example 8b
Example 8c
Example 8d
5 Solve the following equations by first expanding the brackets.
a 2(4u + 2) = 52 b 3(3j − 4) = 15 c 5(2p − 4) = 40
d 15 = 5(2m − 5) e 2(5n + 5) = 60 f 26 = 2(3a + 4)
6 Solve the following equations involving negative numbers.
a −6(4p + 4) = 24 b −2(4u − 5) = 34 c −2(3v − 4) = 38
d 28 = −4(3r + 5) e −3(2b − 2) = 48 f −6 = −3(2d − 4)
7 Solve the following equations by expanding and combining like terms.
a 4(3y + 2) + 2y = 50 b 5(2l − 5) + 3l = 1 c 4(5 + 3w) + 5 = 49
d 49 = 5(3c + 5) − 3c e 28 = 4(3d + 3) − 4d f 58 = 4(2w − 5) + 5w
g 23 = 4(2p − 3) + 3 h 44 = 5(3k + 2) + 2k i 49 = 3(2c − 5) + 4
8 Solve the following equations by expanding brackets on both sides.
a 5(4x − 4) = 5(3x + 3) b 6(4 + 2r) = 3(5r + 3) c 5(5f − 2) = 5(3f + 4)
d 4(4p − 3) = 2(4 + 3p) e 2(5h + 4) = 3(4 + 3h) f 4(4r − 5) = 2(5 + 5r)
g 4(3r − 2) = 4(2r + 3) h 2(2p + 4) = 2(3p − 2) i 3(2a + 1) = 11(a − 2)
9 Solve the following equations systematically.
a 2(3 + 5r) + 6 = 4(2r + 5) + 6 b 3(2l + 2) + 18 = 4(4l + 3) − 8
c 2(3x − 5) + 16 = 3 + 5(2x − 5) d 3(4s + 3) − 3 = 3(3s + 5) + 15
e 4(4y + 5) − 4 = 6(3y − 3) + 20 f 3(4h + 5) + 2 = 14 + 3(5h − 2)
PROBLEM-SOLVING AND REASONING
10, 11, 14 11, 12, 14, 15
11–13, 15, 16
10 Desmond notes that in 4 years’ time his age when doubled will give the number 50 .
Desmond’s current age is d .
a Write an expression for Desmond’s age in 4 years’ time.
b Write an expression for double his age in 4 years’ time.
c Write an equation to describe the situation described above.
d Solve the equation to find his current age.
11 Rahda’s usual hourly wage is $w . She works for 5 hours at this wage and then three more hours at
an increased wage of $(w + 4) .
a Write an expression for the total amount Rahda earns for the 8 hours.
b Rahda earns $104 for the 8 hours. Write and solve an equation to find her usual hourly wage.
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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