This document contains practice problems for solving two-step equations. It provides 16 practice problems with step-by-step solutions for solving equations with addition, subtraction, multiplication and division. It also includes 3 word problems involving equations and their solutions. The document is from a mathematics textbook and aims to help students practice and learn techniques for solving two-step equations.

1. MSM07G7_RESBK_Ch12_003_010.pe 1/29/06 8:44 PM Page 4
Name Date Class
LESSON Practice B
12-1 Solving Two-Step Equations
Solve. Check each answer.
1. 7x ؉ 8 ‫63 ؍‬ 2. ؊3y ؊ 7 ‫2 ؍‬ 3. 4a ؊ 13 ‫91 ؍‬
x‫4؍‬ ‫3؊ ؍‬ a‫8؍‬
4. 6a ؊ 4 ‫2؊ ؍‬ 5. 5k ؉ 2 ‫6 ؍‬ 6. 9m ؊ 14 ‫8؊ ؍‬
1 4 2
a ‫ ؍‬ᎏᎏ
3
k ‫ ؍‬ᎏᎏ
5
m ‫ ؍‬ᎏᎏ
3
Solve.
v u z
7. ᎏᎏ ؊ 3 ‫5 ؍‬
4
8. ᎏᎏ ؉ 3 ‫1 ؍‬
5
9. 6 ؉ ᎏᎏ ‫9 ؍‬
9
v ‫23 ؍‬ u ‫01؊ ؍‬ z ‫72 ؍‬
f w e
10. ؊7 ؉ ᎏᎏ ‫1؊ ؍‬
2
11. 9 ؉ ᎏᎏ ‫5؊ ؍‬
4
12. ᎏᎏ ؊ 3 ‫5؊ ؍‬
7
f ‫21 ؍‬ w ‫65؊ ؍‬ e ‫41؊ ؍‬
d u f
13. ؊8 ؉ ᎏᎏ ‫2 ؍‬
5
14. ᎏᎏ ؉ 3 ‫6 ؍‬
5
15. ᎏᎏ ؉ 5 ‫8 ؍‬
؊3
d ‫05 ؍‬ u ϭ 15 f ‫9؊ ؍‬
16. Two years of local Internet service costs $685, including
the installation fee of $85. What is the monthly fee?
$25 per month
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
4 Holt Mathematics

2. LESSON Practice A LESSON Practice B
12-1 Solving Two-Step Equations 12-1 Solving Two-Step Equations
Solve each equation. Cross out each number in the box that Solve. Check each answer.
matches a solution.
1. 7x ؉ 8 ‫63 ؍‬ 2. ؊3y ؊ 7 ‫2 ؍‬ 3. 4a ؊ 13 ‫91 ؍‬
6 ؊8 ؊4 ؊6 ؊18 ؊3 2 4 8 3 18
x‫4؍‬ y ‫3؊ ؍‬ a‫8؍‬
1. 5x ؉ 8 ‫32 ؍‬ 2. ؊2p ؊ 4 ‫2 ؍‬ 3. 6a ؊ 11 ‫31 ؍‬
4. 6a ؊ 4 ‫2؊ ؍‬ 5. 5k ؉ 2 ‫6 ؍‬ 6. 9m ؊ 14 ‫8؊ ؍‬
x‫3؍‬ p ‫3؊ ؍‬ a‫4؍‬ 1 4 2
a ‫ ؍‬ᎏᎏ
3
k ‫ ؍‬ᎏᎏ
5
m ‫ ؍‬ᎏᎏ
3
k
4. 4n ؉ 12 ‫4 ؍‬ 5. 9g ؉ 2 ‫02 ؍‬ 6. ᎏᎏ ؉ 8 ‫5 ؍‬
6
Solve.
v u z
7. ᎏᎏ ؊ 3 ‫5 ؍‬
4
8. ᎏᎏ ؉ 3 ‫1 ؍‬
5
9. 6 ؉ ᎏᎏ ‫9 ؍‬
9
n ‫4؊ ؍‬ g‫2؍‬ k ‫81؊ ؍‬
s c a
7. ᎏᎏ ؊ 4 ‫2 ؍‬
3
8. ᎏᎏ ؉ 5 ‫1 ؍‬
2
9. 9 ؉ ᎏᎏ ‫8 ؍‬
6
v ‫23 ؍‬ u ‫01؊ ؍‬ z ‫72 ؍‬
f w e
10. ؊7 ؉ ᎏᎏ ‫1؊ ؍‬
2
11. 9 ؉ ᎏᎏ ‫5؊ ؍‬
4
12. ᎏᎏ ؊ 3 ‫5؊ ؍‬
7
s ‫81 ؍‬ c ‫8؊ ؍‬ a ‫6؊ ؍‬
Solve. Check each answer.
d f ‫21 ؍‬ w ‫65؊ ؍‬ e ‫41؊ ؍‬
10. 3v ؊ 12 ‫51 ؍‬ 11. 8 ؉ 5x ‫2؊ ؍‬ 12. ᎏᎏ ؊ 9 ‫3؊ ؍‬
4 d u f
13. ؊8 ؉ ᎏᎏ ‫2 ؍‬
5
14. ᎏᎏ ؉ 3 ‫6 ؍‬
5
15. ᎏᎏ ؉ 5 ‫8 ؍‬
؊3
v‫9؍‬ x ‫2؊ ؍‬ d ‫42 ؍‬
d ‫05 ؍‬ u ϭ 15 f ‫9؊ ؍‬
13. An electrician charges $50 to come to your house. He also charges $25 for each
hour he spends at your house. The electrician charges you a total of $125. How
many hours did he spend at your house? 16. Two years of local Internet service costs $685, including
the installation fee of $85. What is the monthly fee?
3 hours $25 per month
Copyright © by Holt, Rinehart and Winston.
All rights reserved. 3 Holt Mathematics Copyright © by Holt, Rinehart and Winston.
All rights reserved. 4 Holt Mathematics
LESSON Practice C LESSON Reteach
12-1 Solving Two-Step Equations 12-1 Solving Two-Step Equations
Solve. Check each answer. You can solve two-step equations by undoing one operation at
a time. First undo any addition or subtraction, then undo
1. 15h ؊ 4 ‫6 ؍‬ 2. 25k ؉ 12 ‫31؊ ؍‬ 3. 8m ؊ 14 ‫7؊ ؍‬
any multiplication or division.
2 7 Complete the steps to solve each equation.
h ‫ ؍‬ᎏᎏ m ‫ ؍‬ᎏᎏ
3 k ‫1؊ ؍‬ 8 1. 7x ؉ 3 ‫13 ؍‬
4. ؊5m ؊ 6 ‫48 ؍‬ 5. 3f ؉ 8 ‫82 ؍‬ 6. 5z ؉ 6 ‫02؊ ؍‬ 7x ؉ 3 ؊ 3 ‫؊ 13 ؍‬ 3 Subtract 3 from both sides to undo addition.
7x ‫82 ؍‬
2 1 7x 28 7
ᎏᎏ ‫ ؍‬ᎏ ᎏ
f ‫6 ؍‬ᎏ ᎏ Z ‫5؊ ؍‬ᎏᎏ 7 7
Divide both sides by to undo multiplication.
m ‫81؊ ؍‬ 3 5
x‫4؍‬
Solve. Check
d a 3 3
7. ᎏᎏ ؊9 ‫5 ؍‬ 8. ᎏᎏ ؉ 20 ‫81 ؍‬ 9. ᎏᎏ ؊ 9p ‫ ؊ ؍‬ᎏᎏ 7x ؉ 3 ‫13 ؍‬
14 35 4 5
7( 4 ) ؉ 3 ‫13 ؍‬
?
Substitute 4 for x.
3 28 ؉ 3 ‫13 ؍‬
p ‫ ؍‬ᎏᎏ
?
d ‫691 ؍‬ a ‫07؊ ؍‬ 20
31 ‫ߜ 13 ؍‬
?
4 is a solution.
2 d 2 1 f 1 2 v
10. ؊2ᎏᎏ ؉ ᎏᎏ ‫ ؍‬ᎏᎏ
3 6 3
11. ؊ᎏᎏ ؉ ᎏᎏ ‫ ؍‬ᎏᎏ 12. ؊ᎏ ‫ ؉ 6 ؍‬ᎏ3
ᎏᎏ
3
ᎏ
2.
n
ᎏᎏ ؊ 8 ‫4 ؍‬ 3. 8a ؊ 5 ‫11 ؍‬ 4.
w
9 ؉ ᎏᎏ ‫21 ؍‬
4 8 2 - 6 2
n w
ᎏᎏ ؊ 8 ؉ 8 ‫؉ 4 ؍‬ 8 8a ؊ 5 ؉ 5 ‫؉ 11 ؍‬ 5 9؊ 9 ؉ ᎏᎏ ‫؊ 21 ؍‬ 9
6 2
n 16 w 3
ᎏᎏ ‫21 ؍‬ 8a ‫؍‬ ᎏᎏ ‫؍‬
d ‫02 ؍‬ f‫6؍‬ v ‫02 ؍‬ 6
n 8a 16
2
w
6 • ᎏᎏ ‫21 • 6 ؍‬
΋ ΋
6
ᎏᎏ ‫ ؍‬ᎏᎏ
8 8
2 • ᎏᎏ ‫؍‬
΋ ΋
2
2 • 3
Translate each equation into words, and then solve the equation. n‫؍‬ 72 a‫؍‬ 2 w‫؍‬ 6
n
13. 7 ؉ ᎏᎏ ‫01 ؍‬
2
14. 4w ؊ 9 ‫5؊ ؍‬
7 more than one half a number 4 times a number, minus 9,
Solve.
equals 10; n ‫6 ؍‬ equals ؊5; w ‫1 ؍‬ 5. 4n ؉ 11 ‫72 ؍‬
z
6. ᎏᎏ ؊ 6 ‫3 ؍‬ 7. 3 ؊ 2k ‫7؊ ؍‬
7
15. A taxi charges $1.50 plus a fee of $0.60 for each mile traveled. If a ride costs
$5.40, how many miles was the ride?
1
n‫4؍‬ z ‫36 ؍‬ k‫5؍‬
6ᎏᎏ miles
2
Copyright © by Holt, Rinehart and Winston.
All rights reserved. 5 Holt Mathematics Copyright © by Holt, Rinehart and Winston.
All rights reserved. 6 Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved. 60 Holt Mathematics