Algebra I Chapter 1 HW Answer Keys

Name

Class

1-1

Date

Practice

Form G

Variables and Expressions

Write an algebraic expression for each word phrase. 1. 10 less than x than x x 2 10

2. 5 more than d

minus f 3. 7 minus f

4. the sum of 11 and k

5

11

7 2 f 5. x multiplied multiplied by 6

7. one fourth of a number n n44

1

k

8. the product of 2.5 and a number t 2.5 ? t

and y 9. the quotient of 15 and y 15 4 y

10. a number q tripled q?3

11. 3 plus the product of 2 and h 1

d

6. a number t divided divided by 3 t 4 3

x ? 6

3

1

12. 3 less than the quotient of 20 and x and x 20 4 x 2 3

2?h

Write a word phrase for each algebraic expression. 13. n

1

14. 5

6

the sum of n and 6 x

16. 4 2 17 17 less than the quotient of x and and 4

2

15. 11.5

c

5 less than c 17. 3 x 1 10

1 y

the sum of 11.5 and y 18. 10 x 1 7z

10 more than the product of 3 and x

the sum of 10 x and and 7 z

Write a rule in words and as an algebraic expression to model the relationship in each table. 19. Te local video store charges a monthly membership fee of $5 and $2.25 per video. Videos ( v )

Cost (c )

1

$7.25

2

$9.50

3

$11.75

$5 plus $2.25 $2.25 times the number of videos; 5 1 2.25v

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3

Name

1-1

Class

Date

Practice (continued)

Form G

Variables and Expressions

20. Dorothy gets paid to walk her neighbor’s dog. For every week that she walks the dog, she earns $10. Weeks (w )

Pay ( p )

4

$40.00

5

$50.00

6

$60.00

$10 times the number of weeks; 10w

Write an algebraic expression for each word phrase. 21. 8 minus the quotient of 15 and y 8 2 15 4 y

22. a number q tripled plus z doubled 3q

1

2 z

23. the product of 8 and z plus the product of 6.5 and y 8 z 1 6.5 y

5 1 d 24. the quotient of 5 plus d and 12 minus w 12 2 w

25. Error Analysis A student writes 5 y ? 3 to model the relationship the sum of 5y and 3. Explain the error. The word “sum” indicates that addition should be used and not multiplication. The student has used the multiplication symbol instead of the 1 . 26. Error Analysis A student writes the difference between 15 and the product of 5 and y to describe the expression 5 y 2 15. Explain the error. The number 15 should be first and the expression should be written 15 2 5 y . 27. Jake is trying to mail a package to his grandmother. He already has s stamps on the package. Te postal worker tells him that he’s going to have to double the number of stamps on the package and then add 3 more. Write an algebraic expression that represents the number of stamps that Jake will have to put on the package. 2 s 1 3

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4

Name

Class

Date

Practice

1-2

Form G

Order of Operations and Evaluating Expressions

Simplify each expression. 1. 42 16

2. 53 125

5 2 25 4. 6 36

5. (1

7. 5

8.

Q162 R

11.

Q205 R

QR Q R 3(2) 11

1

10. 17(2)

2

42 18

14. 25

Evaluate each expression for s

5

s 1

6 8

4

s

19. 4

22.

2

17

4(s )2

2

1 t

3

4

5

23.

9

4(5)

2

42

2

2 t

20. 3(t )3

13

2

2 and t

17. 5

2

3)2 16

1

3

13. (4(5))3 8000

16.

3. 116 1

Q

s 1

9. 44(5)

12

2

10(3)2

4

5

6. (0.1)3 0.001

26

2

22 28

16 15,625

12 3 27 3

R

2 2

3(6) 4 15. 17 2 5 81 16

Q

R

18. 11.5

10 385

2 2

5t 2

Q 278

3(11) 1313

5.

0

1

12.

1

R

21. s 3

24.

or 0.001024

2 15.5

1 s

2 33

1 t

Q 113 (3)5( ) R s

2

2

t

81 49

25. Every weekend, Morgan buys interesting clothes at her local thrift store and

then resells them on an auction website. If she brings $150.00 and spends s , write an expression for how much change she has. Evaluate your expression for s 5 $27.13 and s 5 $55.14. 150

2

s

; $122.87; $94.86


13

Name

Class

Date

Practice(continued)

1-2

Form G

Order of Operations and Evaluating Expressions

26. A bike rider is traveling at a speed of 15 feet per second.

d 5 15.0 s

Write an expression for the distance the rider has traveled after s seconds. Make a table that records the distance for 3.0, 5.8, 11.1, and 14.0 seconds.

Time (s) Distance (ft) 3.0

45.0

5.8

87.0

11.1

166.5

14.0

210.0

Simplify each expression. 27. 4 f (12 2956 30. f (48

5)

2

44g

28. 3 f (4 363

8)3

2

7g 3

31.

1

4

2

6)2

1

7g 2

29. 2.5 f 13 257.5

4)(3) 3 2 5(1) 2512

Q114(

2

9,129,329

R

32. 4 f 11

2

2

2

Q 366 R g

(55

2

35)

4

3g

294.667

33. a. If the tax that you pay when you purchase an item is 12% of the sale price, write an expression that gives the tax on the item with a price p. Write

another expression that gives the total price of the item, including tax. 0.12 3 p ; 0.12 p

1 p

;

b. What operations are involved in the expressions you wrote? multiplication and addition c. Determine the total price, including tax, of an item that costs $75. $84 d. Explain how the order of operations helped you solve this problem. First you have to multiply 0.12 by p to determine the tax, then you have to add the tax to the original sale price. 34. Te cost to rent a hall for school functions is $60 per hour.

60 3 h

Write an expression for the cost of renting the hall for h hours. Make a table to �nd how much it will cost to rent the hall for 2, 6, 8, and 10 hours.

Hours Rental Charge 2

120

6

360

8

480

10

600

Evaluate each expression for the given values of the variables. 35. 4(c 1 5)

2 f

4; c 5

1, f 5 4

36.

2

1 x g

2; w 5

5, x 5 6

147

240

2

2

37. 3.5 f h3 80.5

3 f (w 2 6)2

2

2

Q 36 j R2 g; h

5

3, j 5

38. x f y 2 2 (55 215,658

4

2

5)

2 y

4


14

3g ; x 5

6, y 5 6

2

Name

Class

1-3

Date

Practice

Form K

Real Numbers and the Number Line

Simplify each expression. 1.

!

2.

!

5

3.

!

4.

!

7

5.

!

6.

!

7.

Å 49

8.

Å 144

9.

!

10.

!

144 12

169 13

256 16

9

3 7

0.01 0.1

25

49

400 20

196

7 6

0.49 0.7

Estimate the square root. Round to the nearest integer. 11.

!

12.

!

13.

!

14.

!

15.

!

16.

!

38 6

99 10

23.75 5

65 8

145.5 12

64.36 8

Find the approximate side length of each square �gure to the nearest whole unit. 17. a tabletop with an area 25 ft 2 5 ft 18. a wall that is 105 m2 10 m

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25

Name

Class

Date


1-3

Form K

Real Numbers and the Number Line

Name the subset(s) of the real numbers to which each number belongs. 3 19. 4 rational

20. 28

21. 2π

rational, integer

irrational 2 24. 23

23. ! 11

22. 45,368 rational, natural, whole, integer

irrational

rational

Compare the numbers in each exercise using an inequality symbol. 1 26. 3, ! 1.25

25. ! 36, ! 49 ! 36

R

1 3

! 49

S

! 1.25

34 28. 19 , 1.8

27. ! 100, 2 ! 169 ! 100

R

34 19

2 ! 169

R

1.8

Order the numbers in each exercise from least to greatest. 29. 2.75, ! 25, 2 ! 36

1 30. 1.25, 2 3 , ! 1.25

2 ! 36 , 2.75, ! 25

2 13 , ! 1.25, 1.25

3 31. 5, 20.6, ! 1

80 30 32. 25 , ! 9, 9

20.6, 35 , ! 1

80 30

! 9 , 25 , 9

33. Kate, Kevin, and Levi are comparing how fast they can run. Kate was able to

run 5 miles in 47.5 minutes. Kevin was able to run 8 miles in 74 minutes. Levi was able to run 4 miles in 32 minutes. Order the friends from the fastest to the slowest. Levi, Kevin, Kate


26

Name

Class

Date

Practice

1-4

Form K

Properties of Real Numbers

Match statements 1–8 with the property, a

2

h, that the statement illustrates.

Commutative Property of Addition: Commutative Property of Multiplication: Additive Identity: Multiplicative Identity: Associative Property of Addition: Associative Property of Multiplication: Zero Property of Multiplication: Multiplicative Property of 21:

a b. c. d. e. f. g. h. 1. 12

1

3. 35

? x 5 x ?

5.

1

m

7. (15

917

0

1

917

5

1

05a a ? 1 5 a (a 1 b) 1 c 5 a 1 (b 1 c) (a ? b) ? c 5 a ? (b ? c) a ? 0 5 0 21 ? a 5 2a a 1

?

6. 25

5

0

5

4. ( x ? 3)

c

11

a ? b5 b ? a

2. 5

35 b

5 m

9)

12 a

1

a 1 b5 b 1 a

15

1

(9

1

11) e

8.

1

2

?

?

1

6

0 g

?

5

4

5 x ?

(3 ? 4) f

25 d

6 h

5 2

Simplify each expression. Justify each step that has not been justi�ed. 9. 5

10. 3

1

(

(3 x 1 2)

? x ?

6)

5

5

5

(5

5

7

1

1

1

5

3

5

(3 ? 6)

5

18 x

?

(6

(2

1

2)

3 x )

1

Commutative Property of Addition Associative Property of Addition

3 x

3 x

Combine like terms.

Commutative Property of Multiplication

)

? x

Associative Property of Multiplication

? x

Multiply.


35

Name

Class

Date


1-4

Form K

Properties of Real Numbers

Simplify each expression. Justify each step. 11. (2

1

7m)

1

5

2)

1

5

(7m

5

7m

1

(2

5

7m

1

7

1

12. 9 5

Commutative Property of Addition Associative Property of Addition Combine like terms.

5)

1

?

(r ? 21)

5

9

(21

5

(9

5

189r

?

?

) Commutative Property of Multiplication Associative Property of r Multiplication Multiply.

? r

21)

?

Tell whether the expressions in each pair are equivalent. 13. 2 x and 2 x ? 1

14. (5

equivalent 15. 8

1

6

1

2

2) ? x and 3 x

equivalent

b and 8

1

6b

16. 5

not equivalent

?

(4

2

4) and 0

equivalent

17. You have prepared 40 mL of vanilla, 20 mL of chocolate, and 50 mL of milk for

a milkshake. a. How many milliliters of milkshake will you have if you �rst pour the vanilla, then the chocolate, and �nally the milk into your glass? 110 mL b. How many milliliters of milkshake will you have if you �rst pour the chocolate, then the vanilla, and �nally the milk into your glass? 110 mL c. Explain how you can tell whether the amounts of milkshake described in parts (a) and (b) are equal. Commutative Property of Addition Use deductive reasoning to tell whether each statement is true or false. If it is false, give a counterexample. 18. For all real numbers a and b, a False 7 2 3 u 3 2 7

2

19. For all real numbers p, q, and r , p True

b

5

b

2

q

2

20. For all real numbers x , y , and z , ( x 1 y ) True 21. For all real numbers n, n False 8 1 1 u 8

1

1

5

2

a.

r 5 p

1

2

r 2 q .

z 5 z 1 ( x 1 y ).

n.

22. Writing Explain why the commutative and associative properties do not hold

true for subtraction and division. Answers will vary. Counterexamples: 5 2 3 u 3 2 5; (5 6 4 3 u 3 4 6; (24 4 6) 4 2 u 24 4 (6 4 2)

2

3) 2 2

u

5 2 (3


36

2

2);

Name

Class

Date

Practice

1-5

Form G

Adding and Subtracting Real Numbers

Use a number line to �nd each sum.

1. 4

1

8 12

4.

2

6

1

(22)

2

7.

2

7

1

(27)

2

7

1

8 1

6

1

3

2.

2

8

5.

2

14

8. 9

2

3. 9

1

(24) 5

6. 5

1

(210)

9.

2

8

2

12.

2

11

15.

2

3

1

(29) 0

36

1

1

0

5

2

8

2

Find each sum.

10. 22

1

(214) 8

11.

13. 45

1

77 122

14. 19

1.5

1

1 9

Q 59 R

16.

2

19.

2

1

6.1 4.6

2

17.

2

2.2

2

3 20. 4

2 3

2

1

1

(213)

(230)

1

49

2

(216.7)

Q 38 R

3 8

2

18.9

2

15

1

17 2

18

1

(218)

18. 5.3

1

(27.4)

1 5

1

7 1 10 2

21.

2

22. Writing Explain how you would use a number line to �nd 6 1 (28). Answers may vary. Sample: Start at 0. Move 6 spaces to the right and then 8 spaces to the left. The answer is 22. 23. Open-Ended Write an addition equation with a positive addend and a

negative addend and a resulting sum of Answers may vary. Sample:

10

2

1

2

8.

2

8

5 2

24. Te Bears football team lost 7 yards and then gained 12 yards. What is the

result of the two plays? a gain of 5 yd


43

2

36

2.1

2

Name

Class

Date


1-5

Form G

Adding and Subtracting Real Numbers

Find each difference. 25. 7

2

28. 33

31. 1.7

34.

2

7 8

14

26.

7

2

2 (214)

2

Q 218 R

29. 62

47

2 (23.8)

5.5

3 4

2

32.

m 2 p

5.5

71

2

2

20

9

2

5.8

10.3

2

1 1 2 6

5 24, n 5

38.

2

2

12

24.5 2

2 35. 3

Evaluate each expression for m 37.

28 2

27.

25 2 (216)

30.

225 2 (225)

33.

23.7 2 (24.2)

4 36. 9

5, and p

2m 1 n 2 p

5

2

11

1.5.

7.5

39.

n 1 m 2 p

27 degrees 41. A teacher had $57.72 in his checking account. He made a deposit of $209.54.

Ten he wrote a check for $72.00 and another check for $27.50. What is the new balance in his checking account? $167.76 42. A scuba diver went down 20 feet below the surface of the water. Ten she dove

down 3 more feet. Later, she rose 7 feet. What integer describes her depth? 16

2

43. Reasoning Without doing the calculations, determine whether 247

is greater. Explain your reasoning.

247 2 (233) is greater; 247 2 (233) is the same as which is greater than 247 1 (233).

47

2

1

33


44

0.5

2

What was the change in temperature?

1 (233)

0.5

Q 223 R 119

40. At 4:00 �.�., the temperature was 298 F. At noon, the temperature was 18 8 F.

or 247

0

2 (233)

Name

Class

1-6

Date

Practice

Form G

Multiplying and Dividing Real Numbers

Find each product. Simplify, if necessary. 1.

5(27)

2. 8(211)

2

35

5.

81

?

2 9

11.

1 6

2

2 5

12

5(29)

2

45

9. 8(22.4)

0.36

6.9

2

6.

8. (20.6)2

3(2.3)

3 4

12

36

2

2

3

2

2

10.

3

2

?

108

88

2

4. (29)2

7.

3. 9

19.2

2

2 2 12. 3

Q 58 R

QR

2

1 4

4 9

13. After hiking to the top of a mountain, Raul starts to descend at the rate of 350 1 feet per hour. What real number represents his vertical change after 1 2 hours? 525 ft

2

14. A dolphin starts at the surface of the water. It dives down at a rate of 3 feet per

second. If the water level is zero, what real number describes the dolphin’s 1

location after 3 2 seconds? 2

10 12 ft


! 1600

16.

40

18.

2

! 0.81

19.

4

4

22.

! 1.44

20.

2

! 10,000

! 0.04 0.2

% 49 16

2

4

w100

w1.2

% 9

2 3

w

17.

25

0.9

4

! 625

2

2

21.

2

23.

4 7

% 121 100

10 11


53

Name

Class

Date


1-6

Form G

Multiplying and Dividing Real Numbers

24. Writing Explain the differences among ! 25, 2 ! 25, and 4 ! 25. There are 2 square roots of 25, 5 and 2 ! 25

25.

! 25 represents the positive square root and

represents the negative square root, and

w ! 25

represents both square roots.

25. Reasoning Can you name a real number that is represented by ! 236?

Explain. no; There is no number that can be multiplied by itself and have a negative product.

Find each quotient. Simplify, if necessary. 26.

51

2

29. 84

4

32. 14.4

35. 17

4

217

(24)

4

4

3

221

(23)

24.8

1 3 51

2

30.

2

33.

2

36.

2

Evaluate each expression for a 38.

2ab

3 8

250

27.

93

52

39. b

4

4

1.7

4

3 8

Q

4

(225) 10

28. 98

4

2 49

105 5

221

2

(23) 31

31.

(210) 0.17

34.

2

37.

2

40.

c a

2

9 10

R

5 12

8.1

5 6

4

4

1 2

3

22.7

21

3 1 2 , b 5 4 , and c 5 26 . 4

c 2

1 8

12

1 41. Writing Explain how you know that 25 and 25 are multiplicative inverses. Because

25 3

1 5 5 21,

the two numbers are multiplicative inverses.

42. At 6:00 �.�., the temperature was 55°F. At 11:00 �.�. that same evening, the

temperature was 40°F. What real number represents the average change in temperature per hour? 238 F/h


54

2 3

Name

Class

Date

Practice

1-7

Form G

The Distributive Property

Use the Distributive Property to simplify each expression. 1. 3(h

5)

2

3h 2 15 5. 20(8

20a

2

9. (14

a)

2

9p)1.1

9.9 p

2

3. (6 1 9v )6 54v 1 36

4. (5n 1 3)12 60n 1 36

6. 15(3 y 2 5)

7. 21(2 x 1 4)

8. (7

45 y 2 75

42 x 1 84

160

1

2

2. 7(25 1 m) 7m 2 35

1

10. (2b

15.4

13. (25 x 2 14)(5.1)

2

6.4b 2 32 5 1 14. 1 22 r 2 7

Q

25.5 x 2 71.4

2

2

1 11. 3 (3z 1 12) z 1 4

10)3.2

R

15. 10(6.85 j 1

5 1 2 r 2 7

1

6w )6

36w 1 42 1 12. 4 2 t 2 5 2t 2 20 2 2 2 7.654) 16. 3 3m 2 3

Q

R

Q

R

4 9m

68.5 j 1 76.54

4 9

2

Write each fraction as a sum or difference. 17.

21.

3n

18

1

7 1

6

5 3n

1

5 7

18.

1

4 z 3

22.

7

8z 3

14

2

6 x 14

19

19

2

15n 2 42 15n 14 14

6 x 19

2

19.

3 23.

3d 1 5 d 1 5 2 6 6 56

20.

9p

2

3

6 3 p 2 2

81 f 1 63 28w 7 2 7w 24. 2 8 9

2

9f 1 7


(14

2

)

1 x

26.

14 2 x

8

2

29.

(4m

2

4m

2

2 1

( 8

2 2

6n)

6n

30.

1

2

27.

6t

(5.8a

2

6t )

1

4.2b)

31.

(6

d ) 26 2 d

2

28.

1

(

2 2 x 1 y 2

1)

r 2 1

1)

32.

x 2 y 1 1

5.8a 2 4.2b

2

(

2 2r 1

(

2 f 1

3 g 2 7)

f 2 3g

2

1

7

Use mental math to �nd each product. 33. 3.2

3

3 9.6

34. 5

3

8.2 41

35. 149

37. 4.2

3

5 21

38. 4

3

10.1 40.4

39. 8.25

3

3

2 298

36. 6

4 33

40. 11

3

397 2382

3

4.1 45.1

41. You buy 75 candy bars at a cost of $0.49 each. What is the total cost of 75 candy bars? Use mental math. $36.75 42. Te distance around a track is 400 m. If you take 14 laps around the track, what is the total distance you walk? Use mental math. 5600 m 43. Tere are 32 classmates that are going to the fair. Each ticket costs $19. What is the total amount the classmates spend for tickets? Use mental math. $608


63

Name

Class

Date


1-7

Form G

The Distributive Property

Simplify each expression by combining like terms. 44. 4t 1 6t 10t 47.

2 y 2 5 y

7 y

2

2

50. 2 f 1 7 g 2 6

1

8 g

11b2

45. 17 y 2 15 y 2 y

46.

48. 14n2

49. 8 x 2

2

51. 8 x 1 3

2f 1 15g 2 6

7n2 7n2 2

5 x 2 9

52.

2

4b2

1

10 x 2

2

7b2

2

2 x 2

2

5k 2 6k 2

2

2

12k 1 10

6k 2 2 17k 1 10

3 x 2 6

2

Write a word phrase for each expression. Ten simplify each expression. 53. 2( n

1

1)

54.

two times the sum of a number and one; 2n 1 2

1 55. 2 (4m 2 8) one-half the difference of four times a number and eight; 2m 2 4

5( x 2 7)

2

negative five times the difference of a number and seven; 25 x 1 35

56. Te tax a plumber must charge for a service call is given by the expression 0.06(35 1 25h) where h is the number of hours the job takes. Rewrite this

expression using the Distributive Property. What is the tax for a 5 hour job and a 20 hour job? Use mental math. 2.1 1 1.5h; $9.60; $32.10

Geometry Write an expression in simpli�ed form for the area of each rectangle. 57.

58.

5 x 2 2

59.

22n 1 17

4

24

20 x 2 8 Simplify each expression.

48n

2

1

7 xy 3

2

2

11 xy 4

x 2

3 xy 4 2 7 xy 3

2

2z 4z 3 z 64. z 1 5 2 5 5

5

15 x 2 75

408

60. 4 jk 2 7 jk 1 12 jk 9 jk 62. 8 xy 4

15

17mn

1

4mn

2

2(5ab

2

6)

10ab

61.

2

63.

2

mn

2

1

10mn

12

1

65. 7m2n

1

4m2n2

3m2n

1

4m2n2 2 5m3n2 2 5mn2

2

4mn

2

4m2n

2

5m3n2

2

5mn2

12 x 2 6 2 2 x 2 6. Show your work. 6 12 x 2 6 1 1 1 5 (12 x 2 6) 5 (12 x ) 2 (6) 5 2 x 2 1; 2 x 2 1 u 2 x 2 6 6 6 6 6 Simplify each expression.

66. Reasoning Demonstrate why

67. 4(2h 20h

1 1

1)

1

3(4h

1

7)

25

70. 6( y 1 5) 2 3(4 y 1 2) 26 y 1 24

68. 5(n 2 8) 27n 1 2 71.

(a

2

a

2

2

1

1

3b

6(7

1

2

27)

3b 2 27

2n)

69. 7(3 1 x ) 3 x 1 17 72.

2(5

2

4s

4( x 1 1)

1

3 s 2 11t 2 10


64

2

2

6t )

2

5s

1

t

Name

Class

Date

Practice

1-8

Form G

An Introduction to Equations

Tell whether each equation is true, false, or open. Explain. 1. 45 4 x 2 14 5 22 open; it contains a variable

2.

3. 3(26)

4. (12 1 8) true

1

5

5

false; 3(26) 5.

14n

2

2

7

26

1

5

2

1

(215)

3

5 5 213

7

false; 10

1

2

5

5

2

10

52

5 2

4

(210)

12

5 2

4

6

6. 7k 2 8k 5 215 open; it contains a variable 8. 32

5 2

(215)

2

true

open; it contains a variable 7. 10

42

2

5 5 210

4

(24)

1

6

72

5 2

4

8

1

7

true

Tell whether the given number is a solution of each equation. 9. 3b

6

12.

2

15.

2

2

5

8a

8

5

14

2

13; 27 no

2

12

10.

11n; 2 no

4 x 1 7

2

5

13. 7c 2 (25)

4; 1 no

16. 20

5 2

15; 22 yes

11. 12

5

14

26; 3 yes

14. 25

2

10z 5 15; 21 no

5

1 yes 2 t 1 25; 210

5

2 17. 3 m

1

2

2

5

2 f ; 21 no

7 1 yes 3; 2

Write an equation for each sentence. 18. Te difference of a number and 7 is 8.

n

2

758

19. 6 times the sum of a number and 5 is 16. 6(n

1

5) 5 16

20. A computer programmer works 40 hours per week. What is an equation that relates the number of weeks w that the programmer works and the number of hours h that the programmer spends working? h 5 40w 21. Josie is 11 years older than Macy. What is an equation that relates the age of Josie J and the age of Macy M ? J 5 M 1 11

Use mental math to �nd the solution of each equation. 22. t 2 7

5

10 17

x 26. 4 5 3 12

23. 12

5

v 27. 8 5

5 6

2

2

h

2

2

24. 22

7

1

p

5

30 8

28. 4 x 5 36 9

48

25. 6

29. 12b


73

2 g 5

5

12

60 5

2

6

Name

Class

Date


1-8

Form G

An Introduction to Equations

Use a table to �nd the solution of each equation. 30. 4m

5

2

5

11 4

31.

3d 1 10

2

43

32. 2

24 1

36. 35

5

5

3a

1

8

2

2

33. 5h

2

13

1 37. 4 p

1

6

5

12 5

11

2

34.

8

2

5

3 y 2 2

2 35. 8n

16

1

2

5

5

7z 2 7 6

5

8 8

Use a table to �nd two consecutive integers between which the solution lies. 38. 7t 2 20

5

33

39. 7.5

between 7 and 8

5

3.2

between

2

2.1n

2 and

2

40. 37d 1 48

5

368

between 8 and 9

3

2

41. Te population of a particular village can be modeled by the equation y 5 110 x 1 56, where x is the number of years since 1990. In what year were there 1706 people living in

the village? 2005 42. Open-Ended Write four equations that all have a solution of 210. Te equations

should consist of one multiplication, one division, one addition, and one subtraction equation. Answers may vary. Sample: 2

2 x 5

20; x 5; 4 2 5 2 x 2

14; x 1 3

5 2

7

5 2

43. Tere are 68 members of the marching band. Te vans the band uses to travel to

games each carry 15 passengers. How many vans does the band need to reserve for each away game? 5 vans

Find the solution of each equation using mental math or a table. If the solution lies between two consecutive integers, identify those integers. 44. d 1 8 2

5

48. 6 y 2 13 0

10 13

5 2

45. 3p 2 14 5 9 between 7 and 8

46. 8.3 5 4k 2 2.5 between 2 and 3

49. 15

50.

5

8

1

(2a)

7

3

2

1 3h

5 2

2

10

47. c 2 8 24 51. 21

21

2

2

5

12

5 2

7 x 1 8

between 1 and 2

52. Writing Explain the difference between an expression and an equation. An equation has two different quantities that are equal to each other and an expression does not. An expression can only be simplified whereas an equation can be solved.


74

Algebra I Chapter 1 HW Answer Keys

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