3.1 One-Step Equations and Inverse Operations
Transcript of 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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 2
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 3
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 4
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 5
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 6
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 7
16. 𝑥 = −7
17. 𝑎 = 2
18. 𝑛 = 0
19. 𝑟 =27
40
20. 𝑦 = 15
21. 𝑐 = 0
22. 𝑚 = 6
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 8
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.
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 9
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 10
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 11
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 12
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 13
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 14
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
Chapter 3 – Linear Equations Answer Key
CK-12 Basic Algebra Concepts 15
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