Alg1 RBC Answers A...Chapter 1 1.1 Start Thinking Set up an equation using a variable for the...

Answers

Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers

A1

Chapter 1 1.1 Start Thinking

Set up an equation using a variable for the unknown angle measure. The sum of the three known angle measures plus the fourth angle measure is equal to 360 degrees.

1.1 Warm Up

1. 10− 2. 1− 3. 10−

4. 15− 5. 0 6. 9

1.1 Cumulative Review Warm Up

1. Commutative Property of Addition

2. Associative Property of Multiplication

3. Identity Property of Addition

4. Inverse Property of Multiplication

5. Zero Property

6. Distributive Property

1.1 Practice A

1. 2 5 Write the equation.

2 2 5 2 Subtract 2 from each side.

3 Simplify.

x

x

x

+ =+ − = −

=


4 4 3 4 Add 4 to each side.

7 Simplify.

g

g

g

− =− + = +

=



9 Simplify.

m

m

m

− =− + = +

=



6 Simplify.

d

d

d

+ = −+ − = − −

= −



2 Simplify.

p

p

p

+ =+ − = −

= −



2 Simplify.

k

k

k

− = −− + = − +

=

7. 280 360; 80x x+ = =

8. 329 360; 31x x+ = =


3 24Divide each side by 3.

3 38 Simplify.

t

t

t

=

=

=

10. 7 28 Write the equation


7 74 Simplify.

p

p

p

=

=

=


4 4 3 4 Multiply each side by 4.

12 Simplify.

s

s

s

÷ =÷ × = ×

=


5 5 2 5 Multiply each side by 5.

10 Simplify.

j

j

j

÷ =÷ × = ×

=


Divide each side 6 54by 6.6 6

9 Simplify.

q

q

q

− =− =

−− −= −

14. ( )

( ) ( ) ( )

9 2 Write the equation.

Multiply each side 9 9 2 9

by 9.

18 Simplify.

c

c

c

÷ − =

÷ − × − = × −−

= −

15. 43h = 16. 1w = 17. 15f =

18. 1.2u = − 19. 2t = 20. 14.7m = −

21. 11.25 0.75 ; 15 in.= =

22. 7 12; 19 Ft t− + = = °

23. 645 13,500; 14,145p p− = =

24. Multiplication Property of Equality

Answers

Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A2

1.1 Practice B


Subtract 7 from 7 7 9 7

each side.

16 Simplify.

p

p

p

+ = −

+ − = − −

= −



2 Simplify.

k

k

k

= −+ = − +

=



11 Simplify.

w

w

w

− = +− − = + −

= −

4. ( )( )



7 Simplify.

g

g

g

+ − =+ − + = +

=



5 Simplify.

q

q

q

− = − +− + = − + +

− =

6. ( )

( )


Subtract 12 from 12 12 15 12

each side.

3 Simplify.

s

s

s

− − =

− − − = −

=

7. 124.99 42.50; $167.49x x= − =



4 48 Simplify.

y

y

y

− =− =

− =

9. ( )

( ) ( ) ( )



by 8.

40 Simplify.

r

r

r

÷ − =

÷ − × − = × −−

= −

10. 4 Write the equation.3

3 4 3 Multiply each side by 3.3

12 Simplify.

k

k

k

=

× = ×

=

11.

( ) ( )

7 Write the equation.2

Multiply each side2 7 2

by 2.2

14 Simplify.

z

z

z

=−

× − = × −−−

= −

12. ( )

( ) ( ) ( )



by 1.

9 Simplify.

b

b

b

= ÷ −

× − = ÷ − × −−

− =

13. 100 Write the equation.10

100 10 10 Multiply each side by 10.10

1000 Simplify.

p

p

p

− =

− × = ×

− =

14. 67k = 15. 81d = − 16. h π=

17. 1.5t = − 18. 2v = − 19. 9a =

20. added 23

but should have multiplied by 32 ;−

( ) ( )3 32 23 3 2 24; 4 ; 6p p p− = − − = − = −

21.

22. 52 other plants; Solve either equation 1 25 918 or 20 to find 90.x x x= = = There are

90 plants in the garden. So, 90 18 20 52− − = other plants in the garden.

1.1 Enrichment and Extension

1.

( ) ( )54

5 2

545 2

1710

Write the equation.

10 10 Multiply each side by 10.

10 8 25 Simplify.

10 17 Subtract 8 from each side.

Divide each side by 10.

x

x

x

x

x

+ =

+ =

+ ===

Equation Value of x

0x c+ = increase

cx c− = − stay the same

1x

c= decrease

Answers


A3

2.

( ) ( )9 3

16 4

9 316 4

912

34

Write the equation.


9 12 Simplify.


Simplify.

t

t

t

t

t

=

=

===

3.

( ) ( )

1 22 3

812 3

812 3

196

2 Write the equation.

Change the mixed number to an improper fraction.


6 3 16 Simplify.

6 19 Add 3 to each side.


w

w

w

w

w

w

− =

− =

− =

− ===

4. 1

1 Write the equation.7 4

Change the mixed number 5to an improper fraction.7 4

4 35 Cross multiply.

35Divide each side by 4.

4

m

m

m

m

=−

=−

= −

= −

5. 5

Write the equation.2 6

5Place in the numerator.

2 66 10 Cross multiply.

10Divide each side by 6 .

65

Simplify.3

t

tt

t

t

t

π π

π π

π ππ ππ

=

=

=

=

=

6. 745 8

74 4 4 45 5 8 5 5

710

Write the equation.

Multiply each side by .

Simplify.

x

x

x

÷ = −÷ • = − •

= −

7. 3.2 6.4 Write the equation.

6.4Divide each side by 3.2.

3.22 Simplify.

t

t

t

=

=

=

8. 150 7.5 Write the equation.

150Divide each side by 7.5.

7.520 Simplify.

x

x

x

=

=

=

9. 2.4 6.52 Write the equation.

Multiply each side 2.4 2.4 6.52 2.4

by 2.4.

15.648 Simplify.

w

w

w

+ =

÷ • = •

=

10. 131 180; 49x x+ = =

11. ( )365 5 2 180; 175x x+ = − =

12. ( )6 6 2 180; 120x x= − =

13. 2 47 180; 66.5x x+ = =

14. 2 90 180; 45x x+ = =

15. ( ) ( )2 20 2 10 180; 34x x x x+ + − + = =

16. a. 262.12 mi h b. 419.39 km h

1.1 Puzzle Time

IT WAS A SAPPY ONE

1.2 Start Thinking

Add the hours you spent on homework from Monday through Thursday. Then use a variable to represent the hours you need to spend on homework on Friday, and add this to your previous sum. Set this expression equal to 6.8 and solve.

1.2 Warm Up

1. 24 9x x− 2. 23 4a a+ 3. 22 6y y− +

4. 27 4d d− + 5. 24 14h z+ 6. 25 7y xy+


1. yes 2. no 3. yes 4. yes

1.2 Practice A

1. 2t = 2. 5p = − 3. 6h =

4. 13k = 5. 5b = 6. 2f =

7. 8 h 8. 4r = − 9. 7m =

10. 5w = 11. 28; 40 , 28 , 112° ° °

12. 10; 70 , 70 , 120 , 100° ° ° °

13. 4 3 19; 5x x+ = = 14. 2 7 9; 8x x− = =

Answers


15. 10 6; 123

xx− = =

16. ( )5 4 15; 7x x+ = − = −

17. ( )1.06 2 6.5 16.43; $4.50x + =

18. ( )2 6 24 64; 14; 20 ftx x+ + = =

1.2 Practice B

1. 12t = − 2. 23p = − 3. 12k =

4. 11p = 5. 3b = 6. 3j =

7. 375 34.5 720; 10 hx+ =

8. 1r = − 9. 6x = − 10. 5v = 11. 6q =

12. 7 12; 955

xx+ = − = −

13. 123 60; 24x x x− = =

14. ( )8 3 40; 8x x− = =

15.

16. 15, 17, 19− − −


1. ( ) ( ) ( )2 2 2 2 4 2 6 52;n n n n+ + + + + + = −

16, 14, 12, 10− − − −

2. ( )1 29; 14, 15n n+ + =

3. ( ) ( ) ( ) ( )2 1 2 3 2 5 2 7 200;n n n n+ + + + + + + =

47, 49, 51, 53

4. ( )122 5 2 2 ; 12, 14n n= + +

5. ( ) ( )2 2 2 3 2 4 ; 10, 8, 6n n n+ + = + − − −

6. ( )( ) ( )3 1 70 2 3;

18, 19, 20, 21

n n n n+ + = + + + +

7. 4 3 ; 2, 3, 4, 5, 6n n+ =

1.2 Puzzle Time

IT WAS EXHAUSTED

1.3 Start Thinking

Answers may include but are not limited to situations such as the time it takes to get to a relative’s house compared with the time it takes to get home, speed hiking up a hill compared with speed hiking back down the hill, and the time it takes to walk to school compared with the time it takes to ride a bike to school.

1.3 Warm Up

1. 5 25u − 2. 34 17n+ 3. 5 20e− +

4. 3 21t− − 5. 4 24v − 6. 4 20a +


1. 3− 2. 10,000 3. 0

4. 1− 5. 8 6. 0

1.3 Practice A

1. 1x = 2. 2b = 3. 4k = −

4. 2t = 5. 2n = − 6. 3h =

7. 5g = 8. 1w = − 9. 3 h

10. 8; one solutiony = − 11. no solution

12. infinitely many solutions

13. no solution

14. incorrect negative on the right side;

( ) ( )2 5 2 5 ;s s− = + 2 10 2 10;s s− = +

10 10;− = The equation has no solution.

15. a. 25 g b. 2 g

16. 28 17. 1

( )7 2 10 15x− − = Write the equation.

( ) ( )7 2 2 10 15x− − − = Distributive Property

7 2 20 15x− + = Multiply.

2 27 15x− + = Combine like terms.

2 12x− = − Subtract 27 from each side.

6x = Divide each side by 2.−

Answers


A5

1.3 Practice B

1. 8t = − 2. 2u = 3. 1w =

4. 3a = − 5. 5k = 6. 4x =

7. 12x = 8. 5g = − 9. no solution


11. 2; one solutionk =


13. 10 1.5 12.5 ; 5 toppingst t+ = +

14. 2 33 ft; 108 ft , 108 ftSA Vπ π= =

15. 2 32.5 m; 250 ft , 250 ftSA Vπ π= =

16. 14, 15


1. 715x = 2. all real numbers

3. no solution 4. 818y = −

5. Sample answer: 5 7 4 2 3 3x x x− + = + −

6. Sample answer: 5 7t t+ = +

7. Sample answer: 4 3 17x − =

1.3 Puzzle Time

DROP IT A LINE

1.4 Start Thinking

Two numbers that are opposites are the same distance from zero on a number line. Because the distance from 0 to 4 is equal to the distance from 0 to 4,− this proves

that the absolute value of 4 and 4− are both equal to 4.

1.4 Warm Up

1. no; There is no way to score a negative number of points in a basketball game.

2. yes; It is possible for bank accounts to contain a negative amount of money.

3. yes; If you used less electricity this month than last month, the answer would be negative.


1. > 2. < 3. <

4. < 5. > 6. =

1.4 Practice A

1. 2− 2. 0 3. 6 4. 3

5. 5 and 5r r= = −

6. no solution

7. 7 and 3b b= = −

8. 3 and 15k k= = −

9. 7 and 7p p= = −

10. 12 and 12q q= = −

11. 542 and y y= = −

12. no solution

−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7

55

Each solution is 5 units from 0.

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9

55


−4−6−8−10−12−14

−15

−16 −2 0 2

3

4

99

Each solution is 9 units from −6.

−6−8 −5−7 −2−4 −1−3 0 2 41 3 5 6 7 8

77


−14 −12 −10 −8 −6 −4 −2 0 2 4 6 8 10 12 14

1212


−3 −2 −1 0 1 2 3138

54

138

Each solution is units from .138

38

−

Answers


13. a.

b. 7 3x − =

14. 3 and 1j j= − = − 15. 12

1 and f f= − =

16. 135 and b b= = − 17. 2

34 and h h= = −

18. 25 and 1w w= = 19. 5y =

20. no; When 7 is subtracted from each side, the constant becomes negative, so there is no solution, because absolute value cannot be negative.

21. The maximum distance of the race is 10 kilometers and the minimum distance is 5 kilometers.

1.4 Practice B

1. 13 and 7p p= = −

2. 3 and 3k k= = −

3. no solution

4. 15 and 15q q= = −

5. no solution

6. 1432 and m m= − =

7. 953 and g g= =

8. 24 and 18x x= = −

9. 3d =

10. 5 and 1c c= =

11. a. 31 33132 32 321 ; and ;x x x− = = = The

minimum nail length is 3132

inch and the

maximum nail length is 3332

inches.

b. no; 33321.05 >

12. 6 3x − = 13. 5 10x − =

14. 7.5 3.5x − = 15. 6112 and w w= = −

16. 1133 and n n= = − 17. 3

71 and t t= − = −

18. no solution 19. 2j = − 20. 74k = −

21. a. 44 5; 49% and 39%x x x− = = =

b. yes; 50% is not within the range of 39% to 49%.


1. 32x = 2. no solution

3. 7m = 4. 4k =

5. 1x = − 6. 9n =

7. no solution 8. 0x =

−8 −6

−7

−4 −2 0 2 4 6 8 10 12

13

14

1010


−5 −4 −3 −2 −1 0 1 2 3 4 5

33


−20 −15 −10 −5 0 5 10 15 20

1515


−4 −3 −2 −1 0 1 2 3

143

54 6 7

313 3

13

Each solution is units from .313 1

13

−21−18−15−12 −9 −6 −3 0 3 96 12 15 18 2421 27

2121


−1 0 1 2 3 4 5 6 7

The absolute value of an expressionthat equals zero has only one answer.

−1 0 1 2 3 4 5 6 7

22


0 1 2 3 4 5 6 7 8 9 10 11 12

33

halfway point

0 1 2 3

95

5435

Each solution is units from .35

125

35

Answers


A7

1.4 Puzzle Time

IT RESULTED IN THE THRILL OF VICTORY AND THE AGONY OF SEVERAL WEBBED FEET

1.5 Start Thinking

A variable represents a number, so determine what to do using the same logic as if it were a number, and use inverse operations to isolate the variable.

1.5 Warm Up

1. 240 in. 2. 21 cm 3. 37.68 in.


1. 13y = 2. 11p = − 3. 3h =

4. 10x = − 5. 2u = 6. 2.3y = −

1.5 Practice A

1. 4 7y x= − + 2. 5 9y x= +

3. 5 4y x= + 4. 4 9y x= − +

5. 7 35y x= − 6. 2y x= −

7. 3

yx = 8.

10

rx =

9. 3 9

bx

y=

+ 10.

2 11

wx

h=

−

11. 5

4

px

q

+=+

12. 9

3

mx

d

−=−

13. a. 35

90

Cx

−= b. 3; 7 c. 10

14. fm

a= 15.

2

Vh

rπ=

16. b P a c= − −

17. a. 20 years b. $1725 c. 1

Ap

rt=

+

1.5 Practice B

1. 3 8y x= + 2. 18y = −

3. 34 1y x= − + 4. 13

7 1y x= +

5. 10 5y x= + 6. 18 18y x= −

7. 4 5

gx

y=

+ 8.

4 9

wx

a=

−

9. 2

6

zx

p

−=+

10. 10

7

tx

q

−=−

11. kx

a b=

− 12. p s

xq r

−=+

13. 11

4 3

wx

j

−=+

14. 8

1 3

yx

v

+=+

15. x cannot be factored out of the d term; ;k ax bx d= + + ( );k d x a b− = +

k dx

a b

−=+

16. Ir

pt= 17. V

wh

=

18. 2b S a c= − − 19. 2

1 2

Fdk

q q=

20. 2.5 years


1. ( )0

22 3

h h wt

dπ

−= −

2. a. 60.56 sec b. 146.19 sec

3. 206.75 sec

4.

5. Water starts draining quickly and slows down as time goes on; There is more water in the tub at the beginning, so it weighs more, and will be forced down the drain at a faster pace. Over time, the pace of the draining water will slow due to the decreasing volume and weight of the water.

Bonus: no, because π is an irrational number

1.5 Puzzle Time

HE GOT LOCKJAW

Cumulative Review

1. 2− 2. 17− 3. 2 4. 8

5. 17 6. 12 7. 25 8. 2

9. 20− 10. 30 11. 3− 12. 14−

2100

0

35

Answers


13. 38 14. 42 15. 72− 16. 8

17. 4− 18. 16− 19. 19 20. 4−

21. 6 22. 4 23. 8− 24. 7−

25. $9/h 26. 4 packages of diapers

27. $4/gal 28. 7 mi

29. a. 324 ft b. 6 min

30. 2,x = Subtraction Property of Equality

31. 6,y = Addition Property of Equality

32. 8,x = Addition Property of Equality

33. 13,m = Subtraction Property of Equality with the 10, then Division Property of Equality with 1−

34. 9,g = Division Property of Equality

35. 13,b = Division Property of Equality

36. 98,c = Multiplication Property of Equality

37. 30,y = Multiplication Property of Equality

38. 12x = 39. 21w = − 40. 3.6w =

41. 4.6r = 42. 5a π= 43. 15x = −

44. $437 $1087, $650x x+ = =

45. 5 $7.35, $36.75x x÷ = =

46. $7.55 $45.30, 6 packagesx x= =

47. 15 40, 50 candy barsx x− =

48. 0x = 49. 5g = 50. 6w = −

51. 5c = 52. 14x = 53. 16z =

54. 18t = 55. 2w = 56. 4u =

57. 12y = 58. 4x = 59. 1q =

60. 432 43 217; 5 hx= +

61. 158 5 3 ; 51 students per buss= +

62. 810 540 6 ; 45 candy bars per boxb= +

63. 2x = 64. 2t = 65. 9h =

66. 2r = − 67. 1w = 68. 6b = −

69. 1h = 70. 6k = − 71. 3r = −

72. 24x = − 73. 4g = 74. 1t =

75. 1y = − 76. 2y = 77. 4x =

78. 3x = 79. 2 min 80. 4 months

81. no solution 82. no solution

83. 3;x = one solution


85. 2;h = one solution

86. no solution

87. 4 88. 10− 89. 0 90. 14

91. 12− 92. 1 93. 4 94. 5

95. 3, 3r = −

96. no solution 97. no solution

98. 21, 21b = −

99. 6, 2x = −

100. 0, 10w =

101. 5, 5r = −

−5 −4 −3 −2 −1 0 1 2 3 4 5

33


−21−24 −18−15−12 −9 −6 −3 0 3 96 12 15 18 2421

2121


−1−2−3−4−5−6−7−8 0 1 2 3 4

44


−2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12

55


−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7

55


Answers


A9

102. 32, 32y = −

103. 3, 7x = −

104. no solution

105. 0, 4n =

106. no solution

107. 4n =

108. no solution

109. 5, 1v = −

110. 0, 16y =

111. 54.5 1.5; 53 , 56x − = ° °

112. 2 241 2; 39 lb in. , 43 lb in.x − =

113. 16 0.3; 15.7 oz, 16.3 ozx − =

114. 1x = 115. 2, 4x = 116. 1z = −

117. 2 14y x= + 118. 6 2y x= − +

119. 2 5y x= − 120. 4 5y x= − −

121. 1y = − 122. 9 9y x= −

123. 9

yx = 124.

8

mx = 125. w

xu r

=+

126. 50

; 4 months; 7 months30

Cx

−=

Chapter 2 2.1 Start Thinking

Sample answer: the price of a car you could buy, if you have up to $15,000 to spend

2.1 Warm Up

1. = 2. > 3. <

4. > 5. > 6. >


1. 4x = 2. 8p = −

3. 11t = − 4. 109r = −

5. 1x = − 6. 2w =

2.1 Practice A

1. 2x < 2. 4 7m + ≥

3. 10 6q≥ 4. 4 22p >

5. 13 5t ≤ 6. 6 1d> −

7. 65 84x + ≤

8. no 9. yes 10. yes

11. no 12. no 13. yes

14. a. 727x <

b. no; It is not a solution because 750 is not less than 727.

15.

16.

17.

18.

19.

−32−40 −24 −16 −8 0 8 16 24 32 40

3232


−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9

55


−1−2 0 1 2 3 4 5 6

22


0 1 2 3 4 5 6 7 8

The absolute value of an expressionthat equals zero has only one answer.

−5−6−7 −4 −3 −2 −1 0 1 2 3

33


−2 0 2 4 6 8 10 12 14 16 18

88


−3 −2 −1 0 1 2 3 4 65 7 8

−5 −2−4 −3 −1 0 1 2 3 4 5

−5 −2−4 −3 −1 0 1 2 3 4 5

−5 −2−4 −3 −1 0 1 2 3 4 5

−3−4−5−6−7−8−9 −2 −1 0 1 2

Alg1 RBC Answers A...Chapter 1 1.1 Start Thinking Set up an equation using a variable for the...

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