inequalities [111841]Student

Class

Date

1. Which expression represents the statement, "six more than three times x is less than or equal to nine"?  

A. 3x + 6 = ¯9

 

B. 3x + 6 ≥ 9

 

C. 3x + 6 ≤ 9

 

D. 6x + 3 ≤ ¯9

    2. There were 98 projects entered in an art exhibit. The judges chose 12 of those

projects as finalists. The equation shown can be used to find n, the number of projects that were not finalists.

12 + n = 98

Which is another equation that could be used to determine the value of n?

 

A. n = 98 – 12

 

B. n =12  98

 

C. n = 12 + 12

 

D. n = 12 – 98

    3. What is the equation shown solved for y in terms of x?

 

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A.

 

B.

 

C.

 

D.

    4. This model represents the equation x – 8 = 3.

Which model shows the solution to the equation?

 

A.

 

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B.

 

C.

 

D.

    5. At the county fair a person must be at least 54 inches tall to ride the roller coaster.

Howard is h inches tall, and he is tall enough to ride the roller coaster. Which number sentence must be true?  

A. h ≥ 54

 

B. h < 54

 

C. h = 55

 

D. h > 55

    6. In the table, the same rule is used on each number in the a column to get the

number in the b column.

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Which could be the rule used in the table? 

A. 2a + 7

 

B. 3a + 5

 

C. 4a + 3

 

D. 5a + 1

    7. Which expression represents the statement below?

"Seven less than five times y is more than or equal to four."

 

A. 7y – 5 ≤ 4

 

B. 5y – 7 ≥ 4

 

C. 7 – 5y ≥ 4

 

D. 5y –7 ≤ 4

    8. The first five numbers in a pattern are shown below.  

3, 7, 15, 31, 63, ….  

If n represents any number in the pattern, which rule could be used to find the next number?

 

A. n + 4

 

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B. n – 4

 

C. 2n + 1

 

D. 2n – 1

    9. A car traveled a distance of 28 miles on 1 gallon of gas. Which equation could be

used to determine m, the number of miles the car should travel under the same conditions on 15 gallons of gas?  

A. 28 . 1 = 15 . m

 

B. 28 + 1 =15 + m

 

C.

 

D.

    10. Matt needs at least $16 more to buy a bicycle. The cheapest bicycle he can buy

costs $42. Which inequality could be used to find x, the number of dollars Matt has?  

A. x + 42 ≤ 16

 

B. x + 16 ≤ 42

 

C. 16 – x ≤ 42

 

D. 42 + 16 ≤ x

    11. What value of x makes the equation true?

 

A. 180

  B. 27

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C. 3

 

D. 0.8

    12. Which number line represents the inequality?

 

A.

 

B.

 

C.

 

D.

    13. Each of the 24 students in Mrs. Garcia's class will receive the following numbers of

cookies.

2 vanilla cookies 3 butter cookies 4 chocolate cookies

Mrs. Garcia asked her class to write a number sentence using a variable and the information above to solve for the total number of cookies the class will receive. Which of the following should the variable represent?

 

A. The total number of cookies

 

B. The total number of students in the class

  C. The number of cookies each student received

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D. The number of students that will eat their cookies

    14. Which of the following can be used to calculate the perimeter in feet of a square

with sides that each measure x yards long?  

A. 4  (x 3)

 

B. (3 x)  4

 

C. (3 + 4)  x

 

D. 4  x

    15. Which polygon does not have the same perimeter as the others?

 

A.

 

B.

 

C.

 

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D.

    16. Yvonne is controlling a robotic submarine. It is currently ¯53 meters from the ocean

surface. She wants to raise the submarine 18 meters to a new depth, d. The equation below represents this situation.

d = ¯53 + 18

What is the value of d in meters that makes this equation true?

 

A. ¯954

 

B. ¯71

 

C. ¯53

 

D. ¯35

    17. Mrs. Rasheed told her students that they could calculate x, the number of pencils in

her desk, by writing an equation to represent the statement shown and solving it for x.

3 times the sum of x and 5 is 90

Which equation correctly represents this statement?

 

A. (3x) 5 = 90

 

B. 3x + 5 = 90

 

C. 3 (x – 5) = 90

 

D. 3 (x + 5) = 90

    18. In 5 years Anna's age will be twice Hank's age. Which equation could be used to

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find H, Hank's present age if A, Anna's present age, is given?

 

A. A + 5 = 2(H + 5)

 

B. A + 5 = 2H + 5

 

C. A = 2(H + 5)

 

D. A = H + 5

    19. Kelly's shoe size is three sizes smaller than Len's shoe size. If Len's shoe size is

10, which equation can be used to find K, Kelly's shoe size?  

A. K = 10 – 3

 

B. K = 10 × 3

 

C. K = 10 + 3

 

D. K = 3 - 10

    20. Which of these best matches the equation?

4x = 28

 

A. Michael spent $4 on gas. He has $28 left

 

B. Sherree has 28 books. She bought 4 more books.

 

C. The cost of a meal was shared equally by 4 friends. Each friend paid $6.

 

D. Rod wired 4 times as many outlets as light fixtures. He wired 28 outlets

    21. Dan and Paul went shopping at a department store.

Dan spent $4 more than Paul spent.

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Dan spent $24 at the store.

Which equation could be used to calculate p, the amount that Paul spent?

 

A. p − 4 = 24

 

B. 4 • p = 24

 

C. 4 + 24 = p

 

D. 4 + p = 24

    22. Which inequality is graphed on the number line?

 

A. –3 < x < 4

 

B.

 

C.

 

D. – 4< x < 3

    23. Ms. Greene drove 540 miles from Kansas City to Dallas. She drove at an average

rate of 60 miles per hour. The following equation can be used to find the number of hours needed to complete the drive.

60t = 540

How many hours did it take Ms. Greene to drive from Kansas City to Dallas?

 

A. 5

 

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B. 6

 

C. 9

 

D. 10

    24. Bobby and Charlie compared the shells they had collected. The number of shells in

Bobby's bucket was  the number of shells in Charlie's bucket. Which equation shows the relationship between b, the number of shells in Bobby's bucket, and c, the number of shells in Charlie's bucket?  

A.

 

B.

 

C.

 

D.

    25. Which question could be correctly answered by solving the following?

x – 4.80 = 24.00

 

A. Tina has a total of $24.00. If she spends $4.80, what is the value of x, the amount of money she will have left?

 

B. Tina earns $4.80 per hour doing yard work. She earned a total of $24.00 last week. What is the value of x, the number of hours Tina worked last week?

  C. Tina wants to buy a shirt that regularly costs $24.00. She received a discount

of $4.80 off the regular price. What was the value of x, the price of the shirt

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after the discount?

 

D. Tina had $24.00 left after spending $4.80 for lunch. What was the value of x, the amount of money Tina had before lunch?

    26. Which number line best represents the solution of the inequality shown?

x < 3

 

A.

 

B.

 

C.

 

D.

    27. Shelia and 3 of her friends went to a theme park for a day. The total admission cost

was $96 and the total cost for food was $36. If they shared the costs equally, which equation could they have used to determine c, the cost for each person?  

A. 4c = 96 + 36

 

B.

 

C. 3c = 96 + 36

 

D.

    28. Susan purchased several roses for a total of $13.50 and had $29.75 left over. The

equation below can be used to determine the amount of money Susan had before

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purchasing the roses.

x – 13.50 = 29.75

What amount of money did Susan have before purchasing the roses?

 

A. $43.25

 

B. $42.25

 

C. $33.25

 

D. $16.25

    29. Which of the following problem statements models the equation shown?

U – 6 = 55

 

A. Kevin counted a total of 55 candies in 6 jars of the same size.

 

B. Fanny has 55 apples. Gina has 6 fewer apples than Fanny.

 

C. David distributed 55 pencils equally in 5 boxes.

 

D. Diane scored 55 points in Math. Terry scored 6 more points than Diane.

    30. After a discount of $16.25, David paid $48.75 for a pair of shoes. The price of the

shoes before the discount can be determined using the equation below.

x – 16.25 = 48.75

What was the price of the shoes before the discount?

 

A. $32.50

 

B. $52.50

 

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C. $64

 

D. $65

    31. Which number line shows a graph of the inequality below?

x − 3 ≤

 

A.

 

B.

 

C.

 

D.

    32.   33. The equation 2x = 8 is represented by the balance shown.

Which balance shows the value of x that makes the equation true?

 

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A.

 

B.

 

C.

 

D.

    34. Carolyn is climbing a mountain that has a height of 2342 feet. Which equation can

be used to determine h, the height Carolyn has left to climb after she has climbed 829 feet?  

A. h = 829

 

B. h - 829 = 2342

 

C. h + 829 = 2342

 

D. h + 2342 = 829

    35. Cicely earned a total of $60 working at a computer camp. She worked 15 hours.

Which equation could Cicely use to calculate d, the number of dollars per hour she earned?  

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A. d = 60 15

 

B. d 5 = 60

 

C. d = 60.15

 

D. d. 60 = 15

    36. The quadrilateral below is a parallelogram.

Which equation can be used to find the measure in degrees of angle A?

 

A. mA + 41 + 2(138) =360

 

B. mA + 41 + 2(138) =180

 

C. mA + 41 + 138 =360

 

D. 41 + 138 + 138 = 180

    37. Ethan planted vegetables in a rectangular garden that is 8 feet wide and 15 feet

long. There is a 2-foot-wide path around the garden as shown below.

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What is the perimeter of the outside of the path?

 

A. 46 ft

 

B. 62 ft

 

C. 120 ft

 

D. 228 ft 

    38. Elliott traveled 586 miles by train on the way to camp. He will go the rest of the way

by bus. The total distance is 834 miles. Which equation could Elliott use to find b, the number of miles he will travel by bus?  

A. 834 + b = 586

 

B. 834 – b = 586

 

C. 586 b = 834

 

D. 586  b = 834

    39. Sandra has saved $280 more than her sister. If n represents the amount her sister

saved, which expression shows the amount Sandra saved?  

A. 280 + n

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B. 280 > n

 

C. n – 280

 

D. n 280

    40. This year Amy's age is 2 years less than 5 times her nephew's age. Which

expression represents Amy's age in terms of n, her nephew's age?  

A. 2n – 5

 

B. 5 – 2n

 

C. 2 – 5n

 

D. 5n – 2

    41. Dustin built a ramp. The measurements for part of the ramp are shown below.

What is the perimeter in inches of this part of the ramp? 

  A. 63

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B. 98

 

C. 108

 

D. 486

    42. Darla lives 3 times as far from school as Guy does. She lives 15 miles from school.

Which equation can Darla use to find n, the number of miles Guy lives from school?

 

A. 3  n =15

 

B. 3  n =15

 

C. 3  n > n

 

D. 3  15 = n

    43. One of the number patterns in Sally's puzzle book is shown.

4, 16, 64, 256, 1024

Which rule can be used to find each term after the first term in Sally's pattern?

 

A. Square any term to get the next term

 

B. Cube any term to get the next term

 

C. Multiply any term by 2 to get the next term

 

D. Multiply any term by 4 to get the next term

    44. Jordan's garden is shaped like a square with sides that are 10 feet long. If Jordan

enlarges her garden by doubling the length but keeping the width the same, how will the perimeter of Jordan's garden change?  

A. It will be 300 feet longer.

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B. It will be 100 feet longer.

 

C. It will be 20 feet larger.

 

D. It will be 10 feet larger.

    45. Which situation could not be modeled by this equation?

15x + 89 = 119

 

A. A special on eyeglasses offered a base price of $89, with extra features available for $15 each. If the total cost of a pair of glasses was $119, how many extra features were purchased?

 

B. A set of 4 adult tickets to the local team's basketball game was $89. Each additional child's ticket was $15. If a family that bought one adult set paid a total of $119, how many children's tickets did they buy?

 

C. An $89 CD set offered 7 CDs by a popular group. Each additional CD by the group was $15. If the total cost of the CDs that Jimmy's mother bought was $119, how many additional CDs did she buy?

 

D. A customer bought 1 pair of athletic shoes on sale for $89, 1 pair of sunglasses for $15, and some water bottles. If the customer spent $119, how many water bottles did she buy?

    46. Jason had $18. After he saved his allowance for 12 weeks, he had $78. Which

equation can be used to find m, the amount of Jason's allowance?  

A. 18m + 12 = 78

 

B. 18m ÷ 12 = 78

 

C. 12m + 18 = 78

  D. 12m – 18 = 78

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    47. For a school field day, 144 students were assigned to 16 different teams. If each

team had the same number of students, which equation can be used to find t, the number of students on each team?  

A. 144.16 = t

 

B. t + 144 = 16

 

C. 144 16 = t

 

D. t – 16 = 144

    48. Which expression represents the phrase shown?

3 less than 2 times the number n

 

A. n2 – 3

 

B. 3 – n2

 

C. 2n –3

 

D. 3 – 2n

    49. Which problem could be solved using the number sentence below?

5 × c = 35

 

A. Dennis has 35 stickers. Eric has 5 times more stickers than Dennis. How many stickers does Eric have?

 

B. Peter has 35 candies. He distributes them equally among 5 friends. How many candies does each friend receive?

  C. Andy's score on a science quiz is 35. Mary's science-quiz score is 5 more than

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Andy's. What is Mary's science-quiz score?

 

D. Jane has 35 apples. Fiona has 5 fewer apples than Jane. How many apples does Fiona have?

    50. A rectangle has a length of 30 feet and a width of 20 feet. What is the perimeter in

feet of the rectangle?  

A. 600

 

B. 100

 

C. 60

 

D. 50

    51. In the number sentence below, which part is called the variable?

358 ÷ 179 = 2n

 

A. 358

 

B. ÷

 

C. 2

 

D. n

    52. Walt made this table showing the number of dollars he saved each week.

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Which shows t, the total number of dollars Walt could save in w weeks?

 

A. t = w + 75

 

B. t = 76w + 14

 

C. t = 14w + 76

 

D. t = 14w + 62

    53. A survey found that 34 out of every 100 people floss their teeth regularly. Alice

used the equation 0.66n = 165 to find n, the solution to a problem about the data. Which of the following problems could be the one Alice solved?  

A. In a survey, 165 people reported they do not floss their teeth regularly. What is n, the number of people surveyed?

 

B. If 165 people were surveyed, what is n, the number of people who reported they do not floss their teeth regularly?

 

C. In a survey, 165 people reported they floss their teeth regularly. What is n, the number of people surveyed?

 

D. If 165 people were surveyed, what is n, the number of people that do not floss compared to the number of people who do floss?

 

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   54. An electrician charged the same fee for each of 4 service calls he made one day.

He also charged a fee for each of the following tasks he performed.

Installed 5 electrical outlets at $35 each Installed 2 ceiling fans at $60 each Checked 1 furnace for a charge of $45 Replaced 1 light fixture for a charge of $40

The sum of the charges for all of the service calls and tasks performed was $700. Which equation could represent s, the fee charged for 1 service call?

 

A.

 

B.

 

C.

 

D.

    55. Which rule could be used to make this function table?

 

A. x + 0

 

B. 2x + 1

  C. 2x – 1

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D. 3x – 4

    56. Which of these best matches the equation shown?

 

A. Matt has 70 apples. He placed an equal number in 5 baskets.

 

B. Becky spent $5 on lunch. She has $70 left.

 

C. The cost of a trip was shared equally by 5 friends. Each paid $70.

 

D. Each of 5 friends has the same number of trading cards. Altogether they have 70 cards.

    57. A rule for computing the perimeter of a rectangle is shown.

p = 2(l + w)

Which sentence correctly translates this algebraic rule?

 

A. The perimeter is two times the sum of the length and width.

 

B. The perimeter is the sum of length squared and width squared.

 

C. The perimeter is the product of the length and width divided by two.

 

D. The perimeter is the sum of the width and the length divided by two.

    58. Ms. Jackson spent exactly $53 on these purchases at the movie theater last

Saturday.

Tickets for 6 adults Two containers of popcorn for a total of $8

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Six sodas for a total of $12

If each ticket costs the same amount, which equation could be used to determine c, the cost in dollars of one ticket?

 

A. 6.c = 53 – (8 + 12)

 

B. 6 + c + 8 + 12 = 53

 

C. 6.c = 53 + 8 +12

 

D. 6(c + 8 + 12) = 53

    59. Each classroom at La Brea Middle School has 25 student desks. Which expression

shows the total number of desks in n classrooms?  

A.

 

B. 25n

 

C. n – 25

 

D. n + 25

    60. Renée painted a total of 123 rose and daisy petals on a painting. She painted 61

rose petals. Which number sentence could be used to find d, the number of daisy petals Renée painted?  

A. 61 + d = 123

 

B. 123 ÷ 2 = d

 

C. d – 61 = 123

 

D. 61 × 2 = d

    61. Which equation matches the statement below?

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"The sum of a number and 9 is 84."

 

A. m x 9 = 84

 

B. m + 9 = 84

 

C. m + 84 = 9

 

D. m = 84 + 9

    62. What value of x makes the equation below true?

13x = 299

 

A. 23

 

B. 24

 

C. 286

 

D. 312

    63. Which of the following problems could be solved using the number sentence

shown?

32 + m = 61

 

A. Jack has 32 times more marbles than Kyle. Kyle has 61 marbles. How many marbles does Jack have?

 

B. Jack has 61 marbles. Kyle has 32 marbles more than Jack. How many marbles does Kyle have?

  C. Jack has 61 marbles and Kyle has 32 marbles. What is the total number of

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marbles that Jack and Kyle have?

 

D. Jack has 61 marbles. Kyle has 32 marbles less than Jack. How many marbles does Kyle have?

    64. Allison picked up 317 pecans from under one tree and 156 pecans from under

another tree. Which equation could Allison use to find p, the number of pecans she picked up in all?  

A. 317 + 156 = p

 

B. 317 – 156 = p

 

C. 317 156 = p

 

D. 317 156 = p

    65. Tamara used the equation shown to represent the total amount of money she

added to her bank account over a three-month period.

$128 + $162 + n = $450

What value of n makes the equation true?

 

A. $160

 

B. $288

 

C. $290

 

D. $322

    66. Neka had some repairs done on her car. The total bill was $680, including $192 for

parts and tax. She used the equation below to find r, the cost of labor for repairing her car.

r + 192 = 680

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What is the cost of the labor for repairing Neka's car?

 

A. $483

 

B. $488

 

C. $498

 

D. $872

    67.  n the model below, let , and let .

Which equation best represents the model?

 

A. 9h = 18

 

B. 8h = 18

 

C. 7h = 18

 

D. 6h = 18

    68. What value of x makes the equation true?

6.48 + 3.79 = x

 

A. 2.69

 

B. 3.79

  C. 9.17

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D. 10.27

    69. Karen makes and sells beaded necklaces. The table shows the amount she

charges for up to 4 necklaces.

Karen's Necklaces

Part A. Let x represent the number of necklaces, and let y represent the amount charged for the necklaces. Use the information in the table to plot the points on the grid provided. Be sure to label the axes. Draw a dashed line to connect the points.

Part B. Write an equation for the dashed line you drew in part A.

Part C. If the rate stays the same for any number of necklaces purchased, what is the total amount Karen should charge for 15 necklaces? Show or explain how you got your answer.

       70. What value of n will make this statement true?

7n= 91

 

A. 13

 

B. 14

 

C. 84

 

D. 637

    71. From Monday through Thursday, Yani saw 15 different kinds of birds on the school

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playground. On Friday, he did not see any new kinds of birds. Which number sentence shows how many kinds of birds Yani saw from Monday through Friday?  

A. 15 × 0 = 15

 

B. 15 + 0 = 15

 

C. 0 – 15 = 15

 

D. 0 ÷ 15 = 15

    72. What value of x would make the following equation true?

x – 0.89 = 65.2

 

A. 64.31

 

B. 65.09

 

C. 66.09

 

D. 74.10

    73. A model for this equation is shown below.

m – 2 = 3

Which model shows the solution to the equation?

 

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A.

 

B.

 

C.

 

D.

    74. A restaurant made a sandwich that had a length of 5.7 meters. The sandwich was

then cut into equal lengths that were 0.15 meters each to make smaller sandwiches. The equation below can be used to determine x, the total number of

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smaller sandwiches made.

5.7 = 0.15x

What was the total number of smaller sandwiches made from the 5.7 meter-long sandwich?

 

A. 5

 

B. 38

 

C. 85

 

D. 855

    75. What value of x satisfies the equation below?

x + 9 = 27

 

A. 3

 

B. 18

 

C. 36

 

D. 243

    76. Monica's research paper needs to be 11 pages in length. She has written 4 pages.

The equation below can be used to find p, the number of pages she still needs to write.

4 + p = 11

How many pages does Monica still need to write?

 

A. 4

  B. 7

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C. 8

 

D. 15

    77. What value of y makes this equation true?

13 • y = 65

 

A. 78

 

B. 52

 

C. 25

 

D. 5

    78. What value of x makes the equation true?

x – 4.5 = 9.82

 

A. 14.32

 

B. 13.32

 

C. 5.32

 

D.

    79. Shara bought x postcards for $0.35 each before going on vacation and the same

number of postcards for $0.23 each while she was on vacation. The equation below can be used to determine the number of postcards bought at each price before tax.

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0.35x + 0.23x = 6.96

What was the total number of postcards Shara bought while on vacation? 

 

A. 12

 

B. 18

 

C. 24

 

D. 30

    80.

What number should go in the to make the number sentence true?

 

A. 108

 

B. 55

 

C. 54

 

D. 3

    81. What value of x makes the equation true?

x +179 = 1432

 

A. 1235

 

B. 1253

 

C. 1363

 

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D. 1611

    82. Trena used a balance scale to model an algebra equation. She placed blocks made

from different materials on the balance until the total mass on each side was equal. The top face of each block was labeled with its mass in grams as shown.

The blocks labeled with an x had equal, but unknown, masses. What was the mass in grams of one block labeled x?

 

A. 7.5

 

B. 8

 

C. 8.5

 

D. 16

    83. What value of m makes this equation true?

m – 18 = 35

 

A. 17

 

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B. 43

 

C. 53

 

D. 59

    84. Which value of n makes the equation true?

42 + n = 51

 

A. 19

 

B. 11

 

C. 9

 

D. 7

    85. What value of p makes the equation true?

 36 = p – 8

 

A. 28

 

B. 34

 

C. 40

 

D. 44

    86. The number of eggs sold at a grocery store in December was more than twice the

combined number of eggs sold in October and November. Which inequality correctly relates D, the number of eggs sold in December, to O and N, the numbers of eggs sold in October and November?

  A. D 2( O + N )

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B. D < 2( O + N )

 

C. D  2( O + N )

 

D. D  2( O + N )

    87. Kara is looking in a catalog for a gift for her mother. She plans to spend at least

$15, but not more than $45, including tax. Which inequality represents x, the range of amounts that Kara plans to spend on the gift?  

A. 15  x  45

 

B. 15  x  45

 

C. 15  x  45

 

D. 15  x  45

    88. Jonathan went to the post office to buy $0.37 stamps. Which inequality can be used

to determine s, the greatest number of stamps that Jonathan can buy with $6.00?

 

A. $0.37s ≤ 6.00

 

B. $0.37s > 6.00

 

C. $0.37 + s ≤ 6.00

 

D. $0.37 + s > 6.00

    89. Which inequality has a solution set represented by the graph below?

 

A. ¯ 2 < x

 

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B. ¯ 2 x

 

C. ¯ 2 > x

 

D. ¯ 2 x

    90. Which inequality is equivalent to the given word sentence?

A number, x, is greater than eight.

 

A. x > 8

 

B. x < 8

 

C. x ≤ 8

 

D. x ≥ 8

    91. Which number line best represents the inequality below?

−4 ≤ x

 

A.

 

B.

 

C.

 

D.

    92.  The graph shows the range of tide levels that occurred on a certain day in Snug

Harbor.

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If t is the tide level on that day, which pair of inequalities does the graph best represent?

 

A. t 7 and t 12

 

B. t  7 or t

 

C. t 7 and t 12

 

D. t 7 or t 12

    93. The table below shows the costs of renting a canoe.

Canoe Rental Charges

Which inequality can be used to calculate h, the greatest number of hours that a canoe can be rented with $85?

 

A. 15h – 30  85

 

B. 30h – 15  85

 

C. 15 + 30h  85

 

D. 30h + 15  85

    94. Which graph best represents the solution set to this inequality?

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¯4 ≤ × ≤ 4

 

A.

 

B.

 

C.

 

D.

    95. Joyce has $8.00 to buy packages of drawing paper. Each package costs $1.37

including tax. Which inequality should Joyce use to solve for p, the greatest number of packages of drawing paper she can buy with $8.00?

 

A. 1.37p 8

 

B. 1.37p  8

 

C.

 

D.

    96.   97.   98.   99.   100.   

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