Foundation Worksheet
6:02 Equations with Grouping
Symbols
Name:
Class:
Examples
1 Expand.
a 4(x − 3) = 4 × x − 4 × 3
= 4x − 12
2 Expand, then solve.
a 3(y − 4) = 24
3y − 12 = 24
3y = 36
∴ y = 12
b 7(3c + 5) = 7 × 3c + 7 × 5
= 21c + 35
b 5(2h + 1) = 35
10h + 5 = 35
10h = 30
∴h=3
Exercise
1 Expand.
a 5(x + 3)
d 8(3m − 1)
g 6(2y + 1)
j 8(2x + 1)
b 7(a − 4)
e 4(k − 7)
h 5(4x − 3)
k 7(t − 5)
2 Expand, then solve.
a 2(a + 3) = 8
d 8(x + 5) = 80
g 3(r + 1) = 33
j 10(2a − 3) = 50
m 6(d − 10) = 18
p 3(b + 5) = 36
b
e
h
k
n
q
5(m − 1) = 10
4(2y − 3) = 20
2(x − 4) = 30
2(3t + 5) = 10
5(x + 2) = 40
2(3c − 5) = −4
c
f
i
l
9(2y + 3)
3(q + 8)
10(4n + 5)
12(c + 1)
c
f
i
l
o
r
7(2n + 1) = 21
8(7k − 3) = 144
9(c + 6) = 63
3(4y + 3) = 63
7(m − 4) = 56
5(2p − 1) = −25
Fun Spot 6:02 | What bear goes around scaring other animals?
Expand these, then match the letters with the answers below.
B 4(a + 5)
E 7(a − 4)
H 5(2a − 1)
N −2(2a − 3)
O −4(a + 2)
T −3(4a + 3)
−a + 4
3a + 18
−4a + 6
−4a + 6
I 3(a + 6)
W −(a − 4)
3a + 18
7a − 28
!
−12a − 9
10a − 5
Answers can be found in the Interactive Student CD.
INTERNATIONAL MATHEMATICS 4 FOUNDATION WORKSHEETS
7a − 28
4a + 20
29
−4a − 8
−4a − 8
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(a division of Pearson Australia Group Pty Ltd)
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IM4_Ch06_3pp.fm Page 141 Friday, March 13, 2009 4:54 PM
2 Expand each set of grouping symbols
and then solve the equations.
a 3(a + 7) = 4(a − 2)
b 3(x + 4) + 2(x + 5) = 4
3a + 21 = 4a − 8
3x + 12 + 2x + 10 = 4
− 3a − 3a
Collect like terms.
21 = a − 8
5x + 22 = 4
+8 +8
− 22 − 22
29 = a
5x = −18
∴ a = 29
÷5 ÷5
∴ x = −3 3--5-
Exercise 6:02
Just take it
one step at a time.
Foundation Worksheet 6:02
Equations with grouping symbols
1 Expand these grouping symbols.
a 5(x + 3)
b 7(a − 4)
c 9(2y + 3)
2 Solve these equations.
a 2(a + 3) = 8 b 5(m − 1) = 10 c 7(2n + 1) = 21
1
Expand the grouping symbols and then
solve each equation. (Answers are all integers.)
a 4(x + 1) = 20
b 8(a − 3) = 56
c 6(y − 3) = 18
d 3(2x + 1) = 21
e 5(3 − 4m) = 75
f 7(2b + 3) = 12b − 9
g a + 1 = 3(5 − 2a)
h 9(2x + 3) = 3(7x − 1)
i 14 + 4(2x − 1) = 2(5x − 2) j 3(5x − 2) + 2(5x − 2) = 5x + 10
2
Solve each equation using the worked examples as a guide.
a 4(x − 3) = 5(x + 1)
b 7(a + 5) = 3(5 − a)
d 4(t − 1) = 2(t + 3)
e 3(2x − 1) = 7(x − 5)
g 9(x − 5) = 4(3x − 1) + 9
h 2(4m − 3) = 5m + 5(2m + 1)
j 3t + 2(6 − 5t) − 4 = 9 − 10t k 5(2a − 1) + 3(2a − 1) = 10
m 4(3a − 1) + 2(5a + 6) = 10 n 6(5 − 3n) + 5(3n + 1) = 5
p 5x + 5(x + 5) − 9 = 0
q 7(1 − 2t) + 5(t − 8) + 5 = 0
c
f
i
l
o
r
Solve each equation. Use Worked Example 2(b) as a guide.
a 3(a + 2) + a + 5 = 15
b 5(m − 1) + 2m = 2
d 3(x + 2) + 2(x − 3) = 10
e 5(p + 1) + 2(p + 4) = 20
g 4(2a + 3) + 2(a − 5) = 22 h 2(2m + 3) + 3(m − 5) = 5
c 2(m + 3) + 5(m + 2) = 23
f 4(t − 2) + 2(t + 5) = 14
i 5(a − 3) + 3(2 + 3a) = 19
3
4
5
6(5 − y) = 3(y + 1)
7(x + 1) = 2(2x − 3)
4(2a + 7) + 3a − 6 = 0
3(5 − 3y) + 12(y + 5) = 90
2(2y − 9) + (y + 8) = 5
4(4 + 3a) + 3(2 − a) = 7
Solve these equations, but first read the warning sign!
a 3(x − 2) − 5(x + 2) = 0
b 7(2a + 3) − 3(a − 5) = 12
c 9(2t − 3) − (t + 5) = 2
d 5(3y − 5) − 6(1 − y) = 11 e 4(6 − 3b) − 2(7b − 1) = 26
f 9(3q + 7) − 6(2q + 5) = 14
g 2(3w + 1) − 3(5 − 4w) = 4(2w + 3)
h 17 − 6(2x − 5) = 17
1
3
1
i --- (4x + 3) − 2(2x − 1) = 7 j --- (8x − 9) − --- (8x − 9) = 15
2
4
4
Try solving these equations, but first read the warning sign!
■ Warning!
a 3(a + 2) − 2(a + 1) = 6
b 5(m + 3) − 4(m + 2) = 10
Remember how to expand
c 5(n + 4) − 3(n − 2) = 30
d 6(a + 2) − 4(a − 1) = 20
with a negative term:
e 4(a + 3) − (a + 2) = 13
f 2·4(p + 5) − (p + 3·8) = 11
−2(x + 4) = −2x − 8
or
−3(a − 1) = −3a + 3
CHAPTER 6 EQUATIONS, INEQUATIONS AND FORMULAE
141