3.1 One-Step Equations and Inverse Operations

Chapter 3 – Linear Equations Answer Key

CK-12 Basic Algebra Concepts 1

3.1 One-Step Equations and Inverse Operations

Answers

1. 𝑥 = −4

2. 𝑥 = 4.3

3. 𝑥 = 3

4. 𝑥 =1

4

5. 𝑥 = 1.6

6. 𝑥 = −15

6

7. 𝑥 = 15

24

8. 𝑥 = 1,100

9. 𝑞 = 0

10. 𝑥 = 1.9001

11. 𝑥 =1

7

12. 𝑥 = −1

6

13. 𝑓 = 1

14. 𝑦 = −11

2

15. 𝑟 =1

16

16. 𝑏 =2

3



3.2 Applications of One-Step Equations

Answers

1. a) 10 + 𝑛 = 25, 𝑛 = 15

b) 𝑤 =10

8

c) 𝑟 =𝑛

𝑤, 𝑟 =

1510

8

= 12 𝑤𝑒𝑒𝑘𝑠

2. a) 𝑢 = 3(8.5 + 1.25), 𝑢 = $29.25

b) 𝑐 =𝑢

12, 𝑐 =

$29.25

12, 𝑐 = $2.44

c) 𝑤 = 𝑢 − $9.75, 𝑤 = $29.25 − $9.75, 𝑤 = $19.50

3. a) (question ‘b’ from Ex C) 𝑥 =53.5

12= 4.86

𝑑𝑜𝑔𝑠

𝑚𝑖𝑛𝑢𝑡𝑒

b) (question ‘c’ from Ex C) 𝑥 = 53.5 − 3 = 50.5𝑑𝑜𝑔𝑠

𝑚𝑖𝑛𝑢𝑡𝑒



3.3 Two-Step Equations and Properties of Equality

Answers

1. Answers will vary: Like terms are terms including the power(s) of the same variable(s) Like

terms: 3𝑥𝑦, 12𝑥𝑦, −7𝑥𝑦 Unlike Terms: 3𝑥𝑦, 3𝑥, 3𝑦, 3𝑥2𝑦

2. Answers will vary: The coefficient is the constant (number) by which the variable(s) is/are

multiplied.

3. 32𝑥

4. 13𝑥2 + 26𝑥

5. 15𝑥𝑦 + 12𝑥

6. 8𝑎𝑏 + 9

7. −2𝑚𝑛2 − 9𝑚𝑛 + 8

8. −5𝑦 − 9 = 74

−5𝑦 = 74 + 9

𝑦 =83

−5

𝑦 = −16.6

9. 𝑥 = 20 ∶ 1.3(20) − 0.7(20) = 12

10. 𝑥 = 0.75 ∶ 6(. 75) − 1.3 = 3.2

11. 𝑥 =3

2∶ 5 (

3

2) − (3 (

3

2) + 2) = 1

12. 𝑥 = −11

4∶ 4 ((−

11

4) + 3) = 1

13. 𝑞 = 18

15∶ 5 (1

8

15) − 7 =

2

3

14. 𝑥 = 31

18∶

3

5(3

1

18) +

5

2=

2

3

15. 𝑠 = 11

3∶ 1

1

3− (

3

8(1

1

3)) =

5

6



16. 𝑦 = −110 ∶ 0.1(−110) + 11 = 0

17. 𝑞 = 3 ∶5(3)−7

12=

2

3

18. 𝑞 =43

5∶

5((43

5)−7)

12=

2

3

19. 𝑡 = 3 ∶ 33(3) − 99 = 0

20. 𝑝 = 64

5∶ 5 (6

4

5) − 2 = 32

21. 𝑥 = 7 ∶ 14(7) + 9(7) = 161

22. 𝑚 =6

7∶ 3 (

6

7) − 1 + 4 (

6

7) = 5

23. 𝑥 = 1 ∶ 8(1) + 3 = 11

24. 𝑥 = 9 ∶ 24 = 2(9) + 6

25. 𝑘 = 99 ∶ 66 =2

3(99)

26. 𝑎 = −6

8∶

5

8=

1

2(−

3

4) + 1

27. 𝑑 = −7 ∶ 16 = −3(−7) − 5

28. $79.14

29. 62

3

30. $189

31. 10 ≥ 2.35 + .75𝑚 ∶ 𝑚 ≤ 10.2 𝑚𝑖𝑙𝑒𝑠

32. 300 ≥ 150 + 3𝑔 : He can invite a maximum of 50 guests



3.4 Multi-Step Equations with Like Terms

Answers

1. 𝑓 = 0

2. 𝑥 =15

7

3. 𝑦 = 25

4. 𝑥 + (𝑥 + 2) + (𝑥 + 4) + (𝑥 + 6) = 244 ∶ 58, 60, 62, 64

5. 2

3𝑥 + 4 = 22 ∶ 𝑥 = 27

6. 3.50 = 𝑝 + 1.5𝑝 + (𝑝 + 1.4) ∶ 𝑝 = $0.60

7. 𝑙 =𝑑

5∶ 𝑙 =

65

5∶ 𝑙 = 13

8. 𝑐 = 0.07𝑝 ∶ 5,389.12 = 0.07𝑝 ∶ 𝑝 = $76,987.43



3.5 Distributive Property for Multi-Step Equations

Answers

1. 𝑥 = 9

2. 𝑤 = −22.5

3. 𝑥 = 31

2

4. 𝑎 =2

21

5. 𝑖 = 12

15

6. 𝑣 = 41

8

7. 𝑝 = 9

8. 𝑚 = 1

9. 𝑛 = 8

10. 𝑣 =4

5

11. 𝑏 = 13

12. 𝑣 = −2

5

13. 𝑠 = 6

14. 𝑚 = 0

15. 𝑘 = −2



16. 𝑥 = −7

17. 𝑎 = 2

18. 𝑛 = 0

19. 𝑟 =27

40

20. 𝑦 = 15

21. 𝑐 = 0

22. 𝑚 = 6



3.6 Equations with Variables on Both Sides

Answers

1. 𝑥 = 9

2. 𝑥 = −22.5

3. 𝑥 = 31

2

4. 𝑎 =7

12

5. 𝑡 = −34

9

6. 𝑣 =141

80

7. 𝑦 = −82

29

8. 𝑧 = −32

87

9. 𝑞 = −232

15

10. 𝑏 = 1

11. 𝑥 = 0

12. 𝑣 = 3

13. 𝑘 = −2

14. 5𝑥 − 3 = 3(𝑥 + 5): 𝑥 = 9

15. 5𝑝 + 6 = 9(𝑝 − 4) − 2 ∶ 𝑝 = $11 : Sale price = $7

16. Jaime and George will have the same amount of money in apx 7 ½ weeks

17. a)The plans cost the same at 680 texts. b)At 3000 texts, the flat-rate Plan B is cheaper.

18. a)The rentals cost the same at apx 19 1/3 hrs. b)For a 24-hour time period, the $150/day plan

from Modern Rental is less expensive.



3.7 Equations with Ratios and Proportions

Answers

1. 150: 3 = 50: 1

2. 150: 175 = 6: 7

3. 200: 60 = 10: 3

4. 10: 14 = 5: 7

5. 4.5: 1 = 4.5 hot dogs per minute

6. 20: 1 = 20 pounds per square inch

7. 1: 4 =1 computer per 4 students

8. 30: 1 = 30 students per teacher

9. 3: 1 = 3 meters per floor

10. 1.2: 1 = 1.2 minutes per appointment

11. 5

1=

30

6

12. extremes: 5, 84 means: 12, 35

13. 𝑥 = 24

13

14. 𝑥 = 20.16

15. 𝑥 = 39

19

16. 𝑥 = 500

17. 𝑥 = 7,425

18. 𝑥 =11

162≈ 0.068



19. 𝑥 = 0.4225

20. 𝑥 = 19.19

21. 𝑥 =36

55≈ .655

22. 𝑥 = −24.75

23. 𝑛 = −23

24. $2,270

25. Mount Yukon is 5,960 meters tall

26. 2

15 of the students have a phone less than one year old

27. The new price is 17

13 times the price of the old one. The old one is

13

20 as expensive as the new

one.

28. 5.80

0.879≈ 6.6, you can buy six notebooks, with some cash left over

29. 31

2 cups mix and 2

5

8 cups water

30. 661 nitrogen atoms

31. 35 games



3.8 Scale and Indirect Measurement Applications

Answers

1. Similar figures are exactly the same shape, but may be difference in size or scale.

2. Corresponding angles of similar figures are equal. Corresponding sides are proportional.

3. Indirect measurement is the process of measuring an object by comparing it to a similar figure

and evaluating the proportional sides. Indirect measurement is particularly useful when an

object is difficult to measure directly. Extremely large or small objects, objects with

inaccessible sides, etc. are all excellent candidates for indirect measurement.

4. The Law of Reflection states, “The angle at which the light reflects off the mirror is the same as

the angle at which it hits the mirror.” When an object is viewed in a mirror, the angles from the

object to the mirror and from the mirror to the viewer are equal.

5. 60.7 inches

6. A 1 mile : 1 mile scale map is actual size, and a cartographer would need an inordinate volume

of paper to map any significant area.

7. The tree is apx 16 ft tall

8. Calculated at scale 1.5 in = 7ft:

a) 4.5 in = 21 ft

b) 2 in = 9 ft 4 in

c) 2 in = 9 ft 4 in

d) 1 ¼ in = 5 ft 10 in

e) 1 in = 4 ft 8 in

9. Apx 1252’ 2”

10. 155 miles

11. 4 ft

12. 16 meters

13. 1.5

14. apx 32 ft



3.9 Conversion of Decimals, Fractions, and Percent

Answers

1. 1.1%

2. 0.1%

3. 91%

4. 175%

5. 2000%

6. 16.67%

7. 20.83%

8. 85.71%

9. 157.14%

10. 13.40%

11. 10

91 or apx

1

9

12. 13

20

13. 4

25

14. 1

8

15. 7

8



3.10 Percent Equations

Answers

1. 192

2. $4.50

3. 0.12

4. 46

5. 40

6. 55

7. 625%

8. 3.33%

9. 5000%

10. $14.00



3.11 Percent of Change

Answers

1. $16,125

2. 5.83%

3. 40% discount

4. $300

5. $10.64

6. Store B is the better deal at 1.14 times the wholesale price. Store A charges 1.4 times the

wholesale price.

7. 142 like reality shows



3.12 Formulas for Problem Solving

Answers

1. (5)(8) (ℎ −1

3) = 30 ∶ ℎ =

13

12𝑓𝑡 𝑜𝑟 1′1"

2. 36 = .9(. 8𝑥) ∶ 𝑥 = $50.00

3. 0.06 sec delay

4. $650 on vacation

5. 13.11 𝑐𝑚2

6. 1.91𝐺𝐵

𝑐𝑚2

7. 𝑉 =𝜋(

3

4)

2(5)

3=

15

16𝜋 𝑖𝑛3 ≈ 2.95 𝑖𝑛3

8. 39,370 in

9. 2,172.61 m

10. 12 cm

3.1 One-Step Equations and Inverse Operations

Documents

Transcript of 3.1 One-Step Equations and Inverse Operations