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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