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Solve the equation and describe each step you use.

1. 5x 1 11 5 4x 1 18 2. 11p 2 4 5 6p 1 1 3. 26 5 2(w 1 5)

Solve the equation, if possible.

4. 15x 2 8 5 14x 1 13 5. 9n 2 7 5 5n 1 5 6. 4z 2 15 5 4z 1 11

7. 27a 1 9 5 3a 1 49 8. 4(w 1 3) 5 w 2 15 9. 8( y 2 5) 5 6y 2 18

10. 14m 2 10 5 3(4 1 m) 11. 7 1 x 5 1 }

2 (4x 2 2) 12. 8b 1 11 2 3b 5 2b 1 2

13. 10d 2 6 5 4d 2 15 2 3d 14. 16p 2 4 5 4(2p 2 3) 15. 0.25(8z 2 4) 5 z 1 8 2 2z

Find the perimeter of the square.

16.

5x � 8

3x

17.

10x

6x 1 8

18.

7x � 15

2x

19. Saving and Spending Currently, you have $80 and your sister has $145. You decide to save $6 of your allowance each week, while your sister decides to spend her whole allowance plus $7 each week. How long will it be before you have as much money as your sister?

20. Botanical Gardens The membership fee for joining a gardening association is $24 per year. A local botanical garden charges members of the gardening association $3 for admission to the garden. Nonmembers of the association are charged $6. After how many visits to the garden is the total cost for members, including the membership fee, the same as the total cost for nonmembers?

21. College Enrollment Information about students’ choices of majors at a small college is shown in the table. In how many years will there be 2 times as many students majoring in engineering than in business? In how many years will there be 2 times as many students majoring in engineering than in biology?

Major Number of students enrolled in major Average rate of change

Engineering 120 22 more students each year

Business 105 4 fewer students each year

Biology 98 6 more students each year

Practice BFor use with the lesson “Solve Equations with Variables on Both Sides”

Algebra 1Chapter Resource Book 2-51

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Lesson Solve Multi-Step Equations, continuedamount of space from the ceiling to the top of the first 18 inches of space and the amount of space from the bottom of the bottom shelf to the chair rail. Then count down from the ceiling to get the measurements.

Study Guide

1. x 5 26 2. x 5 25 3. x 5 3 4. x 5 7

5. x 5 4 6. x 5 1 7. x 5 2 8. x 5 26

9. x 5 29 10. y 5 28 11. z 5 25

12. m 5 212

Problem Solving Workshop: Using Alternative Methods

1. 25; 11 2. 7.5 3. 24 4. 4

Challenge Practice

1. 15, 16, 17 2. 20, 22, 24 3. 31, 33, 35

4. 22, 23, 24, 25 5. 34, 36, 38, 40 6. 15, 17, 19, 21 7. 55 8. 65 9. $11.40

Lesson Solve Equations with Variables on Both Sides

Teaching Guide

1. 4x 1 5 5 2x 2 3; this equation has the variable x on both sides of the equal sign. 2. 2x was subtracted from both sides. 3. like terms 4. 2x 1 5 5 23 Combine like terms. 2x 5 28 Subtract 5 from each side. x 5 24 Divide each side by 2.

Alternative Lesson Starter: 2n1 5n 5 200 1 3n; 50 days

Investigating Algebra Activity

1. 4 2. 3 3. 1 4. 2

5. 2x 1 19 5 7x 1 4 Original equation

2x 1 19 2 2x 5 7x 1 4 2 2x Subtract 2x from each side.

19 5 5x 1 4 Simplify.

19 2 4 5 5x 1 4 2 4 Subtract 4 from each side.

15 5 5x Simplify.

3 5 x Divide each side by 5 and simplify.

Practice Level A

1. A. Subtract 4x from each side. B. Add 7 to each side. C. Divide each side by 6. 2. A. Add 2x to each side. B. Subtract 6 from each side. C. Divide each side by 5. 3. A. Distribute 6 to (3x 2 4). B. Add 24 to each side. C. Divide each side by 18. 4. A. Distribute 6 to (x 1 3). B. Subtract 5x from each side. C. Subtract 18 from each side. 5. A. Distribute 4 to (x 2 2). B. Subtract 4x from each side. C. Subtract 1 from each side. D. Divide each side by 3.

6. A. Distribute 4 to (x 2 5). B. Subtract 2x from each side. C. Add 20 to each side. D. Divide each side by 2.

7. 6p 2 3 5 4p 2 1

2p 2 3 5 21 Subtract 4p from each side.

2p 5 2 Add 3 to each side.

p 5 1 Divide each side by 2.

8. 10a 2 2 5 7a 1 4

3a 2 2 5 4 Subtract 7a from each side.

3a 5 6 Add 2 to each side.

a 5 2 Divide each side by 3.

9. 5(m 1 2) 5 20

5m 1 10 5 20 Distribute 5 to (m 1 2).

5m 5 10 Subtract 10 from each side.

m 5 2 Divide each side by 5.

10. x 5 9 11. n 5 2 12. z 5 22 13. a 5 21

14. no solution 15. y 5 10 16. m 5 1

17. x 5 7.2 18. no solution 19. 8 ft

20. Car 1: 6 h

Practice Level B

1. 5x 1 11 5 4x 1 18

x 1 11 5 18 Subtract 4x from each side.

x 5 7 Subtract 11 from each side.

2. 11p 2 4 5 6p 1 1

5p 2 4 5 1 Subtract 6p from each side.

5p 5 5 Add 4 to each side.

p 5 1 Divide each side by 5.

3. 26 5 2(w 1 5)

26 5 2w 1 10 Distribute 2 to (w 1 5).

216 5 2w Subtract 10 from each side.

28 5 w Divide each side by 2.

4. x 5 21 5. n 5 3 6. no solution

Algebra 1Chapter Resource Book A13

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Lesson Solve Equations with Variables on Both Sides, continued 7. a 5 24 8. w 5 29 9. y 5 11 10. m 5 2

11. x 5 8 12. b 5 23 13. d 5 21

14. p 5 21 15. z 5 3 16. 48 17. 80 18. 24

19. 5 weeks 20. 8 visits 21. 3 years; 7.6 years

Practice Level C

1. 9x 2 4 5 7x 2 16

2x 2 4 5 216 Subtract 7x from each side.

2x 5 212 Add 4 to each side.

x 5 26 Divide each side by 2.

2. 5d 2 3 1 2d 5 4d 1 9

7d 2 3 5 4d 1 9 Add 5d and 2d.

3d 2 3 5 9 Subtract 4d from each side.

3d 5 12 Add 3 to each side.

d 5 4 Divide each side by 3.

3. 4(2m 1 5) 5 3m 2 5

8m 1 20 5 3m 2 5 Distribute 4 to (2m 1 5).

5m 1 20 5 25 Subtract 3m from each side.

5m 5 225 Subtract 20 from each side.

m 5 25 Divide each side by 5.

4. 6(7 2 2p) 5 3(5p 1 1)

42 2 12p 5 15p 1 3 Distribute 6 and 3.

42 5 27p 1 3 Add 12p to each side.

39 5 27p Subtract 3 from each side.

13

} 9 5 p Divide each side by 27.

5. 11w 1 2(w 1 1) 5 5w 2 6

11w 1 2w 1 2 5 5w 2 6 Distribute 2 to (w 1 1).

13w 1 2 5 5w 2 6 Add 11w and 2w.

8w 1 2 5 26 Subtract 5w from each side.

8w 5 28 Subtract 2 from each side.

w 5 21 Divide each side by 8.

6. 10 1 2(2a 1 1) 5 7a 2 3

10 1 4a 1 2 5 7a 2 3 Distribute 2 to (2a 1 1).

12 1 4a 5 7a 2 3 Add 10 and 2.

12 5 3a 2 3 Subtract 4a from each side.

15 5 3a Add 3 to each side.

5 5 a Divide each side by 3.

7. 1 }

2 (12n 2 2) 5 5n 2 7

6n 2 1 5 5n 2 7 Distribute 1 }

2 to

(12n 2 2).

n 2 1 5 27 Subtract 5n from each side.

n 5 26 Add 1 to each side.

8. 4y 1 16 5 1 }

3 (10y 2 4)

12y 1 48 5 10y 2 4 Multiply each side by 3.

2y 1 48 5 24 Subtract 10y from each side.

2y 5 252 Subtract 48 from each side.

y 5 226 Divide each side by 2.

9. 2 3 }

4 (8x 2 12) 5 5x 2 2

26x 1 9 5 5x 2 2 Distribute 2 3 }

4 to

(8x 2 12).

9 5 11x 2 2 Add 6x to each side.

11 5 11x Add 2 to each side.

1 5 x Divide each side by 11.

10. n 5 1 11. x 5 22 12. d 5 2

13. w 5 3 14. z 5 210 15. h 5 7 }

10

16. x 5 213 17. no solution 18. x 5 2

19. t 5 15 20. p 5 2.5 21. z 5 2 5 }

13

22. width: 2 units; length: 7 units

23. width: 8 units; length: 11 units

24. 2.48 years 25. 54(x 2 1) 5 42x; 4.5 ft

26. a. 0.06t 5 0.1(t 2 5) b. Yes. The runner from the first group finished the race in about 83 minutes and the runner from the second group

Algebra 1Chapter Resource BookA14

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