NAME DATE PERIOD 3-5 Study Guide and Intervention
NAME ______________________________________________ DATE ______________ PERIOD _____
3-5 Study Guide and Intervention
Solving Two-Step Equations
A two-step equation contains two operations. To solve two-step equations, use inverse operations to undo each operation in reverse order. First, undo addition/subtraction. Then, undo multiplication/division.
Example Solve c 13 7.
2
2c 13 7
c 13 13 7 13
2
Add 13 to each side.
c 20
2
c 2 (20)2 2
Multiply each side by 2.
c 40
Check: c 13 7
2
420 13 7 20 13 7
77
The solution is 40.
For some problems, it may be necessary to combine like terms before solving.
Exercises
Solve each equation. Check your solution.
1. 5t 2 7
2. 2x 5 9
3. 6u 8 28
4. 8m 7 17
1
2
6
3
5. 16 2w 6
6. 50 6d 8
7. 21 42 7k
8. 4a 10 42
5
7
3
13
9. 7c 4 32 10. 12 3m 18
11. 28 2h 18
12. 10 5x 25
4
13. m 6 70
4
256
17. m 9 5
7
98
21. v3 8 22
42
2
14. 5 p 45
2
80
18. k 3 11
9
72
23
15. 18 g 6
3
36
19. 13 a 3
4
64
3
16. 4 n 29
5
125
20. 3 c 12
2
30
22. 8x 16 8x 16
23. 12a 14a 8
2
4
24. 7c 8 2c 17
25. 6 y 42 2y
26. 16 8r 4r 4 24
5
12
1
Lesson 3-5
? Glencoe/McGraw-Hill
127
Glencoe Pre-Algebra
NAME ______________________________________________ DATE ______________ PERIOD _____
3-5 Skills Practice
Solving Two-Step Equations
Solve each equation. Check your solution.
1. 3x 10 1
3
2. a5 8 9
5
4. r 6 5
2
2
5. 18 2q 4
7
7. u 8 8
12
0
8. 7p 11 31
6
10. 4c 20 0
5
11. n 9 5
2
8
13. 2h 10 12
14. 6k 9 15
11
4
16. 12 7y 2
17. 11 3g 32
2
7
19. 2z 4 z 4
20. 10 5h 2 32
8
22. 4a 5 2a 9 44
8
25. 7f 24 25
7
4
23. w3 6 1 2
9
26. 6 m 8 0
6
12
28. 9x 5 4x 20
29. 3 4t 11 2
5
31. 6q 4 16
2
3
32. m8 12 3 12
24
3. 8w 12 4
1
6. 3j 20 16
12
9. 12d 15 3
1
12. 10b 19 11
3
15. w5 4 2
10
18. 12s 13 25
1
21. r7 5 6
7
24. 7k 8k 1
1
27. 10 d 19
9
30. a3 4 9 7
6
33. 5b 6 6b 2 19
11
? Glencoe/McGraw-Hill
128
Glencoe Pre-Algebra
NAME ______________________________________________ DATE ______________ PERIOD _____
3-5 Practice
Solving Two-Step Equations
Solve each equation. Check your solution.
1. 6p 22 10
2. r 4 2
3
2
18
4. 21q 11 10
1
5. v6 1 0
6
7. 8k 40 16
7
8. w 16 5
2
42
10. x 7 9
8
16
11. z 20 20
10
0
13. 9q 10 118
12
14. n 4 10
5
30
16. r 16 2
3
54
17. 9y 11 5y 25
9
19. u9 8 4
36
20. 6h 4 3 h 11
2
22. 18 x 7
3
75
23. 21 9j 10 277
32
25. 1 a9 4 0
27
26. 4w w 26 19
15
3. 5d 9 24
3
6. 7h 20 8
4
9. s 5 1
4
24
12. r2 11 15
8
15. 6w 125 1
21
18. 20 15d 35
1
21. 5p 4p 7
7
24. 12b 9 2b b 87
6
27. 5 4y y 1 23
9
28. RENTAL AGREEMENTS A furniture rental store charges a down-payment of $100 and
$75 per month for a table. Hilde paid $550 to rent the table. Solve 75n 100 550 to
find the number of months Hilde rented the table. 6 months
29. BUSINESS At work, Jack must stuff 1000 envelopes with advertisements. He can stuff
12 envelopes in one minute, and he has 112 envelopes already finished. Solve 1000
12n 112 to find how many minutes it will take Jack to complete the task. 74 min
Lesson 3-5
? Glencoe/McGraw-Hill
129
Glencoe Pre-Algebra
Glencoe Pre-Algebra
A12
? Glencoe/McGraw-Hill
NAME ______________________________________________ DATE ______________ PERIOD _____
3-5 Study Guide and Intervention
Solving Two-Step Equations
A two-step equation contains two operations. To solve two-step equations, use inverse operations to undo each operation in reverse order. First, undo addition/subtraction. Then, undo multiplication/division.
Example Solve }c}
2 }c} 2 13 5 7 2 }2c} 2 13 1 13 5 7 1 13
}c} 5 20 2
12}2c} 2 5 (20)2
c 5 40
13 7. Add 13 to each side.
Multiply each side by 2.
Check: }c} 2 13 5 7 2
}40} 2 13 5 7 2 20 2 13 5 7
75 7 The solution is 40.
For some problems, it may be necessary to combine like terms before solving.
Exercises
Solve each equation. Check your solution.
1. 5t 1 2 5 7
2. 2x 1 5 5 9
3. 6u 2 8 5 28
4. 8m 2 7 5 17
1
2
6
3
5. 16 5 2w 1 6
6. 50 5 6d 1 8
7. 21 5 42 1 7k
8. 4a 2 10 5 42
5
7
3
13
9. 7c 2 4 5 2 32 10. 12 2 3m 5 18
11. 28 5 2h 2 18
12. 2 10 5 2 5x 2 25
4
13. }m} 1 6 5 70 4
256
17. }m} 2 9 5 5 7
98
21. }v} 1 8 5 22 23
42
2
14. 5 1 }p} 5 45 2
80
18. }k} 2 3 5 2 11 9
72
23
15. 18 5 }g} 1 6 3
36
19. 13 1 }a} 5 2 3 4
64
3
16. 4 1 }n} 5 29 5
125
20. 2 3 1 }c} 5 12 2
30
22. 8x 2 16 1 8x 5 16
23. 12a 2 14a 5 8
2
4
24. 7c 2 8 2 2c 5 17
25. 6 5 2 y 1 42 2 2y
26. 16 1 8r 2 4r 1 4 5 24
5
12
1
? Glencoe/McGraw-Hill
127
Glencoe Pre-Algebra
Lesson 3-5
NAME ______________________________________________ DATE ______________ PERIOD _____
3-5 Skills Practice
Solving Two-Step Equations
Solve each equation. Check your solution.
1. 3x 1 10 5 1
3
2. }a} 1 8 5 9 5
5
4. }r} 1 6 5 5 2
2
5. 18 2 2q 5 4
7
7. }u} 2 8 5 2 8 12
0
8. 7p 1 11 5 2 31
6
10. 4c 1 20 5 0
5
11. }n} 2 9 5 2 5 2
8
13. 2h 1 10 5 2 12
14. 6k 2 9 5 15
11
4
16. 12 2 7y 5 2 2
17. 11 2 3g 5 32
2
7
19. 2z 2 4 2 z 5 4
20. 10 2 5h 1 2 5 32
8
22. 2 4a 1 5 2 2a 2 9 5 44
8
25. 7f 2 24 5 25
7
4
23. }w} 1 6 2 1 5 2 23
9
26.
6 2
m }6}
2
8 5
0
12
28. 9x 1 5 2 4x 5 2 20
29. 3 2 4t 1 11 5 2
5
31. 6q 2 4 5 2 16
2
3
32.
m }}
2
12 2
3 5
2 12
8
24
3. 8w 2 12 5 2 4
1
6. 3j 2 20 5 16
12
9. 12d 1 15 5 3
1
12. 10b 2 19 5 11
3
15. }w} 2 4 5 2 2 25
10
18. 12s 1 13 5 25
1
21. }r} 2 5 5 2 6 27
7
24. 7k 2 8k 5 1
1
27. 10 2 d 5 19
9
30.
a }3}
2
4 1
9 5
7
6
33. 5b 1 6 2 6b 1 2 5 19
11
? Glencoe/McGraw-Hill
128
Glencoe Pre-Algebra
Answers (Lesson 3-5)
Glencoe Pre-Algebra
A13
? Glencoe/McGraw-Hill
NAME ______________________________________________ DATE ______________ PERIOD _____
3-5 Practice
Solving Two-Step Equations
Solve each equation. Check your solution.
1. 6p 1 22 5 10
2. }r} 2 4 5 2 3
2
18
4. 21q 2 11 5 10
1
5. }v} 1 1 5 0 26
6
7. 8k 2 40 5 16
7
8. }w} 2 16 5 5 2
42
10. }x} 1 7 5 9 8
16
11. }z} 2 20 5 2 20 10
0
13. 9q 1 10 5 118
12
14. }n} 2 4 5 2 10 5
30
16. }r} 2 16 5 2 3
54
17. 9y 2 11 2 5y 5 25
9
19. }u} 2 8 5 2 4 29
36
20. 2 6h 1 4 2 3 1 h 5 11
2
22. 18 2 }x} 5 2 7 3
75
23. 21 1 9j 2 10 5 2 277
32
25. 1 1 }a} 2 4 5 0 29
27
26. 4w 2 w 2 26 5 19
15
3. 5d 2 9 5 2 24
3
6. 7h 1 20 5 2 8
4
9. }s} 2 5 5 1 4
24
12. }r} 1 11 5 15 22
8
15. 6w 2 125 5 1
21
18. 20 2 15d 5 35
1
21. 5p 2 4p 5 7
7
24. 12b 2 9 1 2b 2 b 5 2 87
6
27. 5 2 4y 1 y 2 1 5 2 23
9
28. RENTAL AGREEMENTS A furniture rental store charges a down-payment of $100 and $75 per month for a table. Hilde paid $550 to rent the table. Solve 75n 1 100 5 550 to
find the number of months Hilde rented the table. 6 months
29. BUSINESS At work, Jack must stuff 1000 envelopes with advertisements. He can stuff 12 envelopes in one minute, and he has 112 envelopes already finished. Solve 1000 5
12n 1 112 to find how many minutes it will take Jack to complete the task. 74 min
? Glencoe/McGraw-Hill
129
Glencoe Pre-Algebra
Answers
Lesson 3-5
NAME ______________________________________________ DATE ______________ PERIOD _____
3-5 R eading to Learn Mathematics
Solving Two-Step Equations
Pre-Activity
How can algebra tiles show the properties of equality?
Do the activity at the top of page 120 in your textbook. Write your answers below.
a. What property is shown by removing a tile from each side?
Subtraction Property of Equality
b. What property is shown by separating the tile into two groups?
Division Property of Equality
c. What is the solution of 2x 1 1 5 9? 4
Reading the Lesson
Write a definition and give an example of the new vocabulary phrase.
Vocabulary
Definition
Example
1. two-step equation
See students' work.
2. To solve two-step equations, use inverse operations to undo each operation in
reverse order.
Helping You Remember
Suppose you start with a number x, multiply it by 2, add three, and the result is 17. The top row of boxes at the right represents the equation 2x 1 3 5 17. To solve the equation, you undo the operations in reverse order. This is shown in the bottom row of boxes.
Start
2
3
x
?
17
2
7
14
So, x 7 .
3 17
Complete the bottom row of boxes in each figure. Then find the value of x.
3.
Start
3
2
x
?
10
4.
Start
5
3
x
?
33
3
2
4
12
10
5
3
6
30
33
5.
Start
2
5
x
?
7
2
5
4
2
7
6.
Start
4
2
x
?
3
4
2
20
5
3
? Glencoe/McGraw-Hill
130
Glencoe Pre-Algebra
Answers (Lesson 3-5)
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