Name
LESSON
Date
Class
Practice C
1-7 Equations and Their Solutions
For each equation, determine whether the given value of the
variable is a solution.
1. 2d 24 for d 8
2. 15 p 6 for p 3
3. x 2 25 for x 5
4. 135 x 9 for x 15
5. 7 t 4 22 for t 20
4s
6. 8 6 for s 12
u
7. 1
5 for u 65
3
8. 2x 3x 60 for x 12
9. 2(100 k) 64 for k 36
10. (69 m) 5 18 for m 3
11. 11 w 11 for w 1
12. 576 n 1,000 for n 524
13. (15 • 6)y 450 for y 5
14. 18c 2 89 for c 11
15. 62 r 20 for r 26
16. x 5 32 for x 2
Replace each ? with a number that makes the equation correct.
17. 28 11 22 ?
18. 19 ?
75 60
19. ? • 12 21 • 4
20. 54 6 108 ?
21. ? 87 46 59
22. 32 • 3 ? • 33
23. Mr. Yakima teaches 4 science classes,
24. Mary put new tiles on her kitchen floor.
with the same number of students in
The floor measures 6 feet long by
each class. Of those students, 80 are
5 feet wide. She used 10 tiles to cover
sixth graders, and 40 are fifth graders.
the entire floor. Each tile was 3 feet
Write an equation to model this situation
long. Write an equation using the
using the variable n. What does your
variable x to model this situation. What
variable represent?
does x represent in the equation?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
59
Holt Mathematics
Practice B
1-7 Equations and Their Solutions
Practice A
1-7 Equations and Their Solutions
LESSON
LESSON
Determine whether the given value of the variable is a solution.
Determine whether the given value of the variable is a solution.
Yes
1. x 1 5 for x 4
3. 2 • v 12 for v 10
No
4. 14 p 2 for p 7
5. 8 w 11 for w 3
Yes
6. 4t 20 for t 5
12
7. s 4 for s 3
No
2. 13 w 10 for w 2
Yes
k
7. 8 4 for k 24
No
Circle the letter of the equation that each given solution
makes true.
9. x 5
A2x7
B 9x3
C 3 • x 18
D 20 x 2
10. g 7
F 9g 16
G 8g1
H 11 g 17
J g11
11. y 2
A 5y8
B 7y1
C3•y6
D 10 y 20
12. m 9
F 10 m 20
G m 4 13
H 7 • m 36
J 18 m 2
13. z 4
A 5z 20
B 12 z 4
C z37
D z84
14. a 8
F 2a 10
G a 12 20
H a44
J 12 a 6
15. Emanuel put 12 marbles on one pan
of a scale. On the other pan, he put
4 marbles, then he added 8 more
marbles to that side. Each of the
marbles weighs 1 ounce. Is the scale
balanced? Explain.
16. Bill and Rhonda have the same
amount of money. Bill has $13.
Rhonda has one $5 bill, three
$1 bills, and one other bill. Is it
a $1 bill or a $5 bill? Explain.
Yes
4. 72 q 8 for q 9
Yes
5. 28 c 43 for c 15
Yes
2. n 12 5 for n 17
Yes
3. 25 • r 75 for r 3
Yes
8. 6 d 15 for d 8
Yes; because 8 4 12
No
1. 9 x 21 for x 11
Yes
No
Yes
8. 16x 48 for x 3
9. 73 f 29 for f 54
No
10. 67 j 25 for j 42
11. 39 v 13 for v 3
Yes
12. 88 d 100 for d 2
13. 14p 20 for p 5
No
15. 7 x 70 for x 10
No
6. u 11 10 for u 111
No
Yes
14. 6w 30 for w 5
No
Yes
16. 6 • n 174 for n 29
Yes
Replace each ? with a number that makes the equation correct.
4
17. 5 1 2 ?
19. ? • 3 2 • 9
18. 10 ?
6
21. ? 8 6 3
12 7
2
20. 28 4 14 ?
1
22. 12 • 0 ? • 15
23. Carla had $15. After she bought
lunch, she had $8 left. Write an
equation using the variable x to
model this situation. What does
your variable represent?
5
0
24. Seventy-two people signed up for the
soccer league. After the players were
evenly divided into teams, there were
6 teams in the league. Write an
equation to model this situation using
the variable x.
15 x 8; x the amount
72 x 6
she spent on lunch
a $5 bill; because
13 5 3 5
57
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Practice C
1-7 Equations and Their Solutions
LESSON
An equation is a mathematical sentence that says that two
quantities are equal.
For each equation, determine whether the given value of the
variable is a solution.
No
3. x 2 25 for x 5
Yes
u
7. 1
5 for u 65
3
4s
6. 8 6 for s 12
No
No
Yes
11. 11 w 11 for w 1
13. (15 • 6)y 450 for y 5
15. 6 r 20 for r 26
Yes
Yes
10. (69 m) 5 18 for m 3
Yes
12. 576 n 1,000 for n 524
No
14. 18c 2 89 for c 11
No
You can write related facts using addition and subtraction.
7 6 13
13 6 7
Yes
8. 2x 3x 60 for x 12
9. 2(100 k) 64 for k 36
Some equations contain variables. A solution for an equation is a
value for a variable that makes the statement true.
Yes
4. 135 x 9 for x 15
Yes
2
No
2. 15 p 6 for p 3
5. 7 t 4 22 for t 20
You can write related facts using multiplication and division.
3 • 4 12
12 4 3
You can use related facts to find solutions for equations. If the related
fact matches the value for the variable, then that value is a solution.
No
Yes
5
16. x 32 for x 2
Replace each ? with a number that makes the equation correct.
17. 28 11 22 ?
19. ? • 12 21 • 4
17
18. 19 ?
7
21. ? 87 46 59
75 60
20. 54 6 108 ?
18
Holt Mathematics
Review for Mastery
1-7 Equations and Their Solutions
LESSON
1. 2d 24 for d 8
58
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
22. 32 • 3 ? • 33
4
12
1
23. Mr. Yakima teaches 4 science classes,
24. Mary put new tiles on her kitchen floor.
with the same number of students in
The floor measures 6 feet long by
each class. Of those students, 80 are
5 feet wide. She used 10 tiles to cover
sixth graders, and 40 are fifth graders.
the entire floor. Each tile was 3 feet
Write an equation to model this situation
long. Write an equation using the
using the variable n. What does your
variable x to model this situation. What
variable represent?
does x represent in the equation?
4n 80 40; n the number
(6 • 5) 3x • 10; x the width
of students in each class
of each tile
A. x 5 9, when x 3
Think: 9 5 x
x4
34
So x 3 is not a solution of x 5 9.
B. x 7 5, when x 12
Think: 5 7 x
x 12
12 12
So x 12 is a solution of x 7 5.
C. 2x 14, when x 9
Think: 14 2 x
x7
97
So x 9 is not a solution for 2x 14.
D. x 5 3, when x 15
Think: 3 • 5 x
x 15
15 15
So x 15 is a solution for x 5 3.
Use related facts to determine whether the given value is a
solution for each equation.
1. x 6 14, when x 8
yes
4. 3a 18, when a 6
yes
2. s 4 5, when s 24
no
no
5. 26 y 9, when y 35 6. b • 5 20, when b 3
yes
no
7. 15 v 3, when v 45 8. 11 p 6, when p 5
yes
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
59
Copyright © by Holt, Rinehart and Winston.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
117
3. g 3 7, when g 11
9. 6k 78, when k 12
yes
no
60
Holt Mathematics
Holt Mathematics