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Date: ________________________
Section 8.1 Extra Practice
1. Solve each equation. Use a number line.
a) 3 x 
3
b)
4
c
4

2
3
2. Solve each equation. Use models of your choice to represent the solutions.
b) 2 x 
a) 3x = 0.6
5
2
3. Solve each equation algebraically.
a) 3x 
2
b)
5
m
5

2
c) –4.5x = 1.35
3
4. Solve each equation. Show a check of each solution.
a) –4x = –4.96
d)
x
2.3
b)
 7.4
x
0.7
 2.1
e) 4m 
10
3
c)
f)
5
m
1
6


1
3
14
m
5. Solve each problem.
a) Carol gave a 15% deposit on a diamond bracelet. The deposit was $73.50. What was the
cost of the bracelet?
b) Eric earned
2
5
of the profits of the canteen on the weekend. His earnings were $620.
What was the total profit earned in the canteen?
c) The density of an object is determined by the formula d 
m
v
, where m is the mass, in
grams, and v is the volume, in litres. What volume does the object occupy if an 8.58-g
object has a density of 3.3 g/L?
d) Jamal received a 20% discount when he purchased his computer. He paid $920. What
was the regular price of the computer?
BLM 8–6 Section 8.1 Extra Practice
1
.
4
2
8
b) c 
, or c  2 .
3
3
5
2. a) x = 0.2 b) x =
4
2
10
1
, or  3
3. a) x 
b) m 
15
3
3
1. a)
a) x = 1.24
b) x = 1.47
c) m = –15
d) x = 17.02
x
e) m =
5
6
f) m = 84
c) x = –0.3
5. a) The bracelet cost $490. b) The canteen earned a $1550
profit. c) The object has a volume of 2.6 L. d) The regular
price of the computer was $1150.
4.
Copyright © McGraw-Hill Ryerson, 2009
Section 8.2 Extra Practice
1. Solve each equation.
a) 2 x 
1 1

4 2
b)
m
 1.5  0.8
2.5
c) 4x – 7 = 29
2. Solve each equation. Then, check your answer.
3
1
 3m 
4
2
x
 4.5
d) 3.4 
1.4
a) 2
1
1 7
x 
2
3 6
1
2
e) 4c +
=
3
6
b)
c)
n
 0.23  1.93
0.6
f) 9.2  0.2x  2.4
3. Create an equation for each of the following. Solve. Then, check.
a) When a number is tripled, then increased by 13, the result is 82. Find the
number.
b) Jane spent $42 for shoes. This was $14 less than twice what she spent for a
blouse. How much was the blouse?
c) The sum of two consecutive numbers is 37. What are the numbers?
d) The cost of a banquet at Nick’s Catering is $215 plus $27.50 per person. If the
total cost of a banquet was $2827.50, how many people were invited?
e) Effie and Kirsten live 23.6 km apart. They decided to cycle to the pool at the
park, which is located between their homes. If Jennifer lives 5.2 km closer to the
park, how far did they each cycle?
f) Hyan has saved $300 more than two-thirds of the cost of the down payment on a
car. If he has $1240 saved, how much is the down payment?
BLM 8–8 Section 8.2 Extra Practice ANSWERS
1. a) x =
5
 5  2 1 5 4
; 4
;

 
6
24
6 6
 24  3
1 1 1
;


6
6
6
3 11
3
3
; 2 2

4
2
4
4
5 1 5 1 7 5 2 7 7 7
b) x =
;
  ;

   ;
3 2 3 3 6 6 6 6 6 6
f) x = –58; –9.2 = 0.2(–58) + 2.4;
–9.2 = –11.6 + 2.4; –9.2 = –9.2
3. a) 3x + 13 = 82. The number is 23.
b) 2x – 14 = 42. The blouse was $28.
c) 2x + 1 = 37. The two consecutive numbers are 18
and 19.
d) 27.50x + 215 = 2827.50. They invited 95 people to
the banquet. e) 2x + 5.2 = 23.6. Effie cycled 9.2 km
and Kirsten cycled 14.4 km.
1
b) m = –1.75 c) x = 9
8
3
3
3 9 2
3 1
2. a) m =
; 2  3   ; 2 
 ;
4
4
4 4 4
4 2
2
c) n = –1.02;
1.02
 0.23  1.93 ;
0.6
1.7 + 0.23  1.93; 1.93 = 1.93
d) x = 1.54; 3.4 
1.54
 4.5 ;
1.4
e) c =
f)
2
x  300  1240 . The down payment is $1410.
3
3.4 + 1.1 = 4.5; 4.5 = 4.5
Copyright © McGraw-Hill Ryerson, 2008
Section 8.3 Extra Practice
1. Show a check for each of the following.
a) 3(x – 5) = 18
b) 0.2(x + 3) = 1.4
c)
x 3
5

2
3
1
3
2. Identify the error in each of the following. Then, write the correct solution.
x 3
4
a) 0.4(x + 2.2) = 5.4
b)
=
5
7
4
 x 3
0.4 x + 2.2 = 5.4
5
 =
7
 5 
4
0.4 x = 3.2
x 3 =
7
17
x=8
x=
7
3. Solve and check each of the following.
a) 2(x – 4) = 12
b) 3(m + 0.5) = –2.1
c) 1.2(x + 1.3) = 2.4
x=4
d)
3
1
( x  8)  7
4
2
x = 11
e)
x  14
1
2
4
2
x=
f)
x  2 7

3
18
4. Solve.
a) The perimeter of a square is 49.2 cm. The side length of the square is
represented by the expression (x + 4.1) cm. What is the value of x?
b) A fraction has a denominator of 20. The numerator has a value of “x less than the
1
denominator.” If the fraction is equivalent to , what is the value of x?
4
c) Two cars leave Calgary at the same time, travelling in opposite directions. Their
average speeds differ by 5 km/h. After 2 h, they are 210 km apart. Find the
speed of each car.
d) A number, plus one-third of itself, plus one-eighth of itself, equals 70. What is the
number?
Copyright © McGraw-Hill Ryerson, 2008
Name: _________________________________
Date: ________________________
.…BLM 1–2.…
(continued)
BLM 8-10 Section 8.3 Extra Practice ANSWERS
1. a) x = 11
Left Side = 3(11 – 5)
= 33 – 15
= 18
Left side = Right Side
b) x = 4
Left Side = 0.2(4 + 3)
= 0.2(7)
= 1.4
Left side = Right side
c) x =
Right Side = 18
Right Side = 1.4
1
3
1

 3  5
3


Left Side = 
Right Side =
2
3
1 9
  5
3 3
= 
10
5
3
10 1
=

3 5
2
=
=
3
Left side = Right side
2. a) The error is that the 0.4 was not distributed into the entire bracket.
0.4(x + 2.2) = 5.4
0.4 x + 0.88 = 5.4
0.4 x = 4.52
x = 11.3
b) The error is that only one side was
multiplied by 5.
x 3 4

5
7
 x  3
4
5
  5 
5


7
20
7
20
x=
3
7
x 3 
20 21

7
7
1
x=
7
x=
3. a) x = 10 b) m = –1.2 c) x = 0.7 d) x = 18 e) x = –4 f) x =
5
6
4. a) The value of x is 8.2 cm. b) The value of x is 15. c) 50 km/h and 55 km/h
d) The number is 48.
Copyright © McGraw-Hill Ryerson, 2008
Section 8.4 Extra Practice
1. Solve and check each of the following.
a) 0.4x = 5.58 – 0.2x
b) 7.2 + 2.3x = 3.2x
x 9 2x
3
 
c)
d) m  m  7
6 2
3
2
x 3
 10
e)
f) 1.4m = 1.5m – 0.57
2
2. Solve and check each of the following.
1
1
3
a) x  1  x 
b) 1.3m + 64.2 = 2.7m + 12.82
2
4
4
1
2
c) 5n – 6.4 = 3n + 2.6
d) n  3  4  n
2
3
1
1
1
e) x  x  x 
f) 1.2m – 17 = 8 + 0.7m
4
3
6
3. Solve and check each of the following.
 m  1   m  2
a)
b) 0.3(2x – 1) – 2.3 = 0.04(x + 5)
2
5
4m  3 3  m

c) 5(2x + 1.2) = 4(x – 1.5)
d)
3
2
4. Create an equation for each of the following. Solve your equation. Then, check your
solution.
a) The length of a rectangular garden is 1 m more than three times the garden’s
width. If the perimeter of the garden is 34 m, find its dimensions.
b) The cash register in the school canteen contains x quarters and (30 – x) dimes. If
the total value of the coins is $5.85, how many of each kind of coin are there?
c) An employee mixes peanuts worth $2.80/kg with cashews worth $3.60/kg. She
sells the mixture for $3.12/kg. If she has 75 kg of peanuts, how many kilograms
of cashews does she need?
d) Plane A leaves the airport. One hour later, Plane B leaves the same airport on the
1
same course. It catches up to Plane A in 2 h. The average speed of Plane B is
2
300 km/h faster than Plane A. Find the speed of each plane.
BLM 8–12 Section 8.4 Extra Practice ANSWERS
c) x = –9
1. a) x = 9.3
Left Side = 0.4(9.3)
= 3.72
Left Side =
Left side = Right side
b) x = 8
Left Side = 7.2 + 2.3(8)
= 7.2 + 18.4
= 25.6
Left side = Right side
Right Side = 5.58 – 0.2(9.3)
= 5.58 – 1.86
= 3.72
Right Side
= 3.2(8)
= 25.6
9 9

6 2
9 27

6
6
36
=
6
=
= –6
Left side = Right side
Copyright © McGraw-Hill Ryerson, 2008
Right Side
=
2(9)
3
=
18
3
= –6
d) m = 14
3(14)
Left Side =
2
42
=
2
Right Side
= 14 + 7
= 21
= 21
Left side = Right side
e) x = 23
23  3
2
20
=
2
Left Side =
Right Side = 10
Right Side
= 8.55 – 0.57
= 7.98
Right Side
1
3
(7) 
4
4
7 3
=

4 4
10
=
4
5
=
2
=
Left side = Right side
b) x = 36.7
Left Side
Right Side
= 1.3(36.7) + 64.2
= 2.7(36.7) + 12.82
= 47.71 + 64.2
= 99.09 + 12.82
= 111.91
= 111.91
Left side = Right side
c) n = 4.5
Left Side = 5(4.5) – 6.4
Right Side = 3(4.5) + 2.6
= 22.5 – 6.4
= 13.5 + 2.6
= 16.1
= 16.1
Left side = Right side
d) n = –42
Left Side =
1
 42  3
2
= –21 – 3
= –24
Left side = Right side
1  2  1  2 

 

4 5  3 5 
Right Side =
1 2

10 15
3 4
=

30 30
7
=
30
2 1

5 6
12
5

30 30
7
=
30
=
Right Side = 8 + 0.7(50)
= 8 + 35
= 43
= 1.5(5.7) –
2. a) x = 7
1
(7)  1
2
7 2
=

2 2
5
=
2
Left Side =
Left side = Right side
f) m = 50
Left Side = 1.2(50) – 17
= 60 – 17
= 43
Left side = Right side
Left side = Right side
Left Side =
2
5
=
= 10
Left side = Right side
f) m = 5.7
Left Side = 1.4(5.7)
0.57
= 7.98
e) x 
2
(42)
3
84
= 4
3
Right Side = 4 
= 4 – 28
= – 24
3. a) m = –3
Left Side = 5(–3 + 1)
= 5(–2)
= –10
Left side = Right side
Right Side
= 2(–3 – 2)
= 2(–5)
= –10
b) x = 5
Left Side = 0.3[2(5)–1] – 2.3
Right Side = 0.04(5 + 5)
= 0.3(9) – 2.3
= 0.04(10)
= 2.7 – 2.3
= 0.4
= 0.4
Left side = Right side
c) x = –2
Left Side = 10(–2) + 6
Right Side = 4(–2) – 6
= –20 + 6
= –8 – 6
= –14
= –14
Left side = Right side
d) m = 3
4(3)  3
3
12  3
=
3
9
=
3
Left Side =
Right Side
33
2
6
=
2
=
=3
=3
Left side = Right side
4. a) The dimensions of the garden are 4 m
by 13 m.
b) There were 19 quarters and 11 dimes in the cash
register.
c) The employee will need 50 kg of cashews for the
mixture.
d) Plane A is travelling at 750 km/h, and Plane B is
travelling at 1050 km/h.
Copyright © McGraw-Hill Ryerson, 2008