1. 22 – 5(6x – 1) = -63
2. 7x – 3(4x + 8) = 11
3. 39 – 12x = 7 – 16x
4. -x – 1 = x – 21
5. 8(4x – 1) – 12x = 11(2x – 6)
6. A triangular sail has a perimeter of 25 m. Side a is 2 meters shorter than twice side b, and side c is 3 meters longer than side b. Find the length of each side.
7. Solve for y: 5x + 2y = 1
8. Solve for y: 8y – 3x = -16
9. Simplify by combining like terms: 3x3 + 9z + 2x3 + 5z + 6x2
10. Angle A twice the size of Angle B. Their sum is 87º. Find x.
11. Solve: 35 x – 6 = 36
12. Tatia has coins in pennies, nickels, dimes, and quarters. The total amount of money she has in dollars can be found by using the expression (P + 5N + 10D + 25Q)/100. Use the table to find how much money she has.
P / N / D / Q20 / 14 / 6 / 12
13. Each month, Ms. Langlinais pays her phone company $28 for her land line, and $0.07 per minute for long distance calls. Write an expression to represent her total bill “y” for a month in which long distance services totaled “h” hours.
14. Xavier took two math tests. He scored 86 points on the second test. This was 18 points higher than his score on the first test. Write and solve an equation to find the score Xavier received on the first test.
15. Jackie earned a mean score of 34,250 points on an online game she played 6 times. Write and solve an equation to determine the total number of points Jackie earned in the 6 games.
16. Bryce has $60 in his savings account. His brother Jonathan has $135 in his. Bryce decides to save $5 of his allowance each week, while Jonathan decides to spend his whole allowance along with $10 of his savings each week. After how many weeks will Bryce and Jonathan have the same amount of money in their savings account? How much will that be?
17. Andres ate 2000 calories in one day. 35% of his calories came from fat. How many of his calories came from fat?
18. Arian works at Home Warehouse. He earns $10 per hour plus 2.75% commission on furniture sales. Last week he worked 25 hours and sold $1527.45 of furniture. Find his pay for last week.
19. At Kroger, a package of microwave popcorn costs $0.49. At a movie theater, the same amount of popcorn is marked up 410%. What is the popcorn’s cost at the movie theater?
20. Solve for j: h-4j = k
21. Find the measure of angle A.
22. The ages of Lauren and two of her friends are three consecutive integers. The sum of their ages is 63. Find Lauren’s age if she is the oldest of the three friends.
23. 50x – 43 = 52x - 81
24. The perimeter of the rectangle below is 82 m. Find the value
of x.
25.
26. x = 8x + 28
27. 12x – 18 = 13x + 18
28. 18x – (8x – 7) = 67
29. The sum of two numbers is 25. The larger number is seven less than seven times the larger number. Find the smaller number.
30. -10 + 52x = -30
31. -1 - 27x = 2
32. 48 = -11x + 18 + 2x
33. Hailey needs to take a taxi to get to the movies. The taxi charges $4.00 for the first mile, and then $2.75 for each mile after that. If the total charge is $20.50, how far was Hailey’s taxi ride to the movies?
34. Delany has $365 in her savings account. She wants to save at least $635. Write, solve and graph an inequality to determine how much more money Delaney must save to reach her goal.
35. Fly with us owns a DC10 airplane that has seats for 240 people. The company flies this airplane only if there are at least 100 people on the plane. Write and graph a compound inequality to show the possible number of people in a flight on a DC10 with Fly with Us.
36. The perimeter of the rectangle is 108 cm. Find the value of x.
5x
x
37. Find three consecutive integers such that twice the greatest integer is 2 less than 3 times the least integer.
38. Find the measure of angle A.
39. Meredith solved the equation below. Where did she make her first mistake?
Given: 2(x + 4) – 6 = x + 22
Step 1: 2x + 8 – 6 = x + 22
Step 2: 2x + 2 = x + 22
Step 3: 3x + 2 = 22
Step 4: 3x = 20
Step 5: x = 20/3
40. Simplify the expression: 3(2x – 6) – 2(4x – 5)
41. Solve and graph: -3x + 2.5x 1.5(x + 4)
42. The cost for renting a movie theater to preview a movie is $575. And, each person must purchase a ticket for $2. Write an equation to find the amount of money “y”, that the movie theater makes if “x” people come to the preview.
43. Write an equation that models the data in the table below:
x / 7 / 9 / 11 / 13f(x) / 5 / 11 / 17 / 23
44. Which equation has infinitely many solutions?
A. 11 – (2v + 3) = -2v – 8
B. 7m – 2 = 8m + 4 – m
C. 5w + 8 – w = 6w – 2(w – 4)
D. 8y + 9 = 8y – 3
45. The two angles below for a right angle. Find the value of x.
46. Simplify: 4(x – 3) – 2(3x – 8)
47. -5 – (15x – 1) = 2(7x – 16) – x
48. 9(11 – x) = -3(3x – 9)
49. 2(6x + 3) = 18 – 3(16 – 3x)
50. Solve and graph: -2 x+23 4
51. The United Postal Service charges a “nonmachinable surcharge” for first-class mail if the length of the envelope (parallel to the address) divided by the height of the envelope is less than 1.3 or more than 2.5. Christi has an envelope with a height of 3.5 inches. Write and graph a compound inequality to show the lengths in inches for which Christi will have to pay the surcharge.
52. Solve and graph: 12x + 3 < -4 or 23x – 1 15
53. Lexi’s car can travel between 380 and 410 miles on a full tank of gas. She filled her tank and drove 45 miles. Write and graph a compound inequality to show how many more miles she can drive without running out of gas.
54. Write an equation that represents the data in the table below:
x / 5 / 4 / 3 / 2 / 1y / 10 / 15 / 20 / 25 / 30
55. The sides of a triangle are consecutive integers. Find the length of the longest side if the perimeter is 66.
56. Compare the values of x in column A and column B. Which statement is true?
Column A Column B
4.2x – 7.3 = -36.7 35x – 0.5 = -4.22
F. The value of x in column A is greater.
G. The value of x in column B is greater.
H. The values are equal.
J. The relationship cannot be determined from the information given.
57. The air temperature stayed steady for several hours and then increased rapidly for a few hours. At the end of the day, a rainstorm came through causing the temperature to drop sharply and then remain constant. Choose the graph that best represents this situation.
58. Graph the following relation:
{(3, 5), (8, -2), (-2, 6), (5, 1), (6, 3), (-4, -2)}
59. Mr. Hahn deposited money into his savings account as follows.
• In June, he deposited 25% of the amount he had at the end of May.
• In July, he deposited 10% of the amount he had at the end of June.
• He made no other deposits or withdrawals.
Let b represent the balance in Mr. Hahn’s savings account at the end of May. Not counting any interest, which of these expressions represents his balance at the end of July?
A. 0.25b + 0.10b C. 0.25b + 0.10(0.25b)
B. b + 0.25b + 0.10b D. 1.25b + 0.10(1.25b)
60. After the last test of the grading period, I plan to use the formula 482+x6 = A to find Aleena’s new test average. What does the x represent in this formula?
61. If y is a function of x in the relationship, y = 3x – 5, which statement is true?
A The independent variable is x, and the dependent variable is y.
B The values of x are elements of the range.
C The independent variable is y, and the dependent variable is x.
D The values of y are elements of the domain.
62. Make a mapping for the relation below. Determine if the relation is a function.
{(5, 8), (3, 2), (5, 9), (3, 8), (6, 8)}
63. Write a possible situation for the graph.
64. A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the number of videos. Identify the independent and dependent variables. Then, write a rule in function notation for the situation.
Give the domain and range of the relation. Tell whether each is a function.
65. 66. 67.
x / y0 / –5
1 / –1
1 / 3
1 / 6
68.
Identify the independent and dependent variables in the situations in 69 and 70.
69. The amount of electricity used for air conditioning in homes increases as the temperature increases.
70. As Kyoko works more hours, her total pay increases.
71. Data was collected on the average winter temperature and the number of days with snow of a random group of cities in the United States. Identify the correlation you would expect to see between the average winter temperature and the number of days with snow.
72. Sylvie is going on vacation. She has already driven 60 miles in one hour. Her average speed for the rest of the trip is 57 miles per hour. How far will Sylvie have driven 7 hours later?
73. Lionel observes that traffic is getting worse and it’s taking him longer to get to work. He records once a week the following data for several weeks. Graph a scatter plot using the given data and give the equation for the line of best fit.
Week / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8Time (min) / 8.2 / 8.9 / 8.6 / 9.3 / 10 / 9.7 / 8.4 / 9.1
73. Graph a scatter plot using the given data and write the equation for the line of best fit.
x / 3 / 6 / 5 / 2 / 7 / 4 / 8 / 1y / 4.5 / 6.5 / 6.5 / 3.5 / 6.5 / 4.5 / 8 / 4
74. Graph a line whose RANGE is all numbers greater than or equal to 6.
75. Graph y = |x| + 6 76. Graph y = x2 -3
Determine if the following are continuous or discrete.
77. A giraffe is born 6 feet tall and continues to grow at a steady rate.
78. The price of a used car is discounted $200 each week.
79. A city planner buys more buses as the population of her city grows.
Give the domain and range of the following. Tell if each is a function.
80. 81. 82.
83. Solve and graph: x + 6 < -1.5
84. Solve and graph: 3x – 8 > 4
85. Solve and graph: 5x – 3(x + 2) 4x – 8
86. For the function f(x) = -4x + 2, find f(x) when x = -8.
87. Write the inequality shown by the graph.
88. Graph -2x + 4y = 4 for the domain D: {–8, –4, 0, 4, 8}.
89. The set of ordered pairs below represents some points on the graph of function f.
{(1, -5), (-7, -29), (-5, -23), (0, -8), (-1, -11)}
What is the parent function of f?
A. y = x C. y = 2x
B. y = x2 D. y = x
90. At a convenience store, the cost, f(x), for x bottles of water is shown by the function f(x) = 1.2x. What does the slope mean in this problem?
91. Which function is not linear?
A. y = 3x C. y = x2 + 2
B. x – y = 1 D. y = 3x4
92. A health insurance plan uses the function f(x) = 5x + 50 to find its cost where x is the number of office visits. What does the y intercept mean in this function?
93. What does the slope mean in the function above?
94. Find the 57th term of the arithmetic sequence: 11, 8, 5, 2, …
95. Find the 40th term of the arithmetic sequence: 8, 14, 20, 26, …
96. Write a function rule for the following: A lawyer is paid 13 of the amount awarded in a lawsuit.
97. Safe cooking temperatures for beef are between 145°F and 170°F inclusive. Write and graph a compound inequality that shows the safe cooking temperatures for beef.