Solve.
36)
When making a long distance call from a certain pay phone, the first three minutes of a call cost
$2.40. After that, each additional minute or portion of a minute of that call costs $0.50. Use an
inequality to find the number of minutes one can call long distance for $10.40.
36)
A)
21 minutes or fewer
B)
19 minutes or fewer
C)
4 minutes or fewer
D)
16 minutes or fewer
Solve the inequality. Other than , graph the solution set on a number line.
37)
4x – 4 3x – 10
37)
A)
(–6, )
B)
(–, –6]
C)
(–, –6)
D)
[–6, )
Solve and graph the solution set on a number line.
38)
x<9
38)
A)
[–9, 9]
B)
(–, –9] [9, )
C)
(–9, 9)
D)
(–, –9) (9, )
Solve and graph the solution set on a number line. Express the solution set in both set–builder and interval notations.
39)
|3x – 3| – 6 < – 8
39)
A)
–, 1
3
B)
1
3, 5
3
C)
–, 5
3
D)
An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
40)
Objective Function z =12x – 14y
Constraints 0
x
5
0
y
8
4x + 5y 30
4x + 3y 20
40)
A)
Maximum: 0; at (0, 0)
B)
Maximum: –55; at (1.25, 5)
C)
Maximum: 60; at (5, 0)
D)
Maximum: –84; at (0, 6)
Graph the inequality in a rectangular coordinate system.
41)
y –5
41)
A)
B)
23
C)
D)
Solve.
42)
ABC phone company charges $19 per month plus 8¢ per minute of phone calls. XYZ phone
company charges $10 per month plus 11¢ per minute of phone calls. How many minutes of phone
calls in a month make XYZ phone company the better deal?
42)
A)
More than 300 minutes
B)
More than 30 minutes
C)
Less than 30 minutes
D)
Less than 300 minutes
Solve the inequality. Other than , graph the solution set on a number line.
43)
4x +1<37
43)
A)
[9, )
B)
( , 9]
C)
( , 9)
D)
(9, )
Graph the inequality.
24
44)
x
4+y
2> 1
44)
A)
B)
C)
D)
45)
x + y –6
45)
A)
B)
C)
D)
26
Find the solution set for the equation.
46)
|6x + 5| + 8 =12
46)
A)
–1
5, –9
5
B)
C)
–1
6, –3
2
D)
1
6, 3
2
Solve.
47)
A certain store has a fax machine available for use by its customers. The store charges $1.75 to send
the first page and $0.50 for each subsequent page. Use an inequality to find the number of pages
that can be faxed for $3.75.
47)
A)
8 pages or fewer
B)
39 pages or fewer
C)
5 pages or fewer
D)
2 pages or fewer
C
Graph the solution set of the system of inequalities or indicate that the system has no solution.
48)
–x +4y <4
x –3
48)
A)
B)
27
C
C)
D)
Solve.
49)
Find the maximum value of the objective function z =24x + 5y subject to the following constraints:
0 x
10, 0
y
5, 3x + 2y 6.
49)
A)
25
B)
240
C)
15
D)
265
Solve and graph the solution set on a number line.
50)
3+1 –x
25
50)
A)
(–, –6] [2, )
B)
(–, –2] [6, )
C)
[–2, 6]
D)
[–6, 2]
Graph the inequality.
28
51)
y 4x + 4
51)
A)
B)
C)
D)
29
Solve the inequality. Other than , graph the solution set on a number line.
52)
x
7–3
5x
2+2
52)
A)
–182
25 ,
B)
, –182
25
C)
, –182
25
D)
–182
25 ,
Graph the inequality.
53)
x – y –5
53)
A)
B)
30
C)
D)
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
54)
x <5 or x <9
54)
A)
(5, 9)
B)
(–, 5)
C)
(–, 9)
D)
(–, 5) (9, )
Solve. Use interval notation to express the range.
55)
On the first four exams, your grades are 78, 98, 57, and 79. There is still a final exam, and it counts
as two grades. You are hoping to earn a C in the course. This will occur if the average of your six
exam grades is greater than or equal to 70 and less than 80. What range of grades on the final exam
will result in earning a C?
55)
A)
[38, 88]
B)
[54, 84)
C)
[38, 88)
D)
[54, 84]
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
56)
x +6<9 and –6x < – 24
56)
A)
(–, 3)
B)
(–, 3) (4, )
C)
(3, 4)
D)
Graph the inequality.
57)
x > – 9
57)
32
A)
B)
C)
D)
Solve the problem.
58)
An office manager is buying used filing cabinets. Each small file cabinet costs $7, takes up 6 square
feet of floor space, and holds 10 cubic feet of files. Each large file cabinet costs $8, takes up 8 square
feet of floor space, and holds 12 cubic feet of files. The total cost cannot exceed $94, and the office
has no more than 84 square feet of floor space available for the cabinets. How many of each file
cabinet should the manager buy to maximize storage capacity? What is the maximum storage
capacity?
58)
A)
0 small file cabinets and 13 large file cabinets; 156 cubic feet
B)
13 small file cabinets and 0 large file cabinets; 130 cubic feet
C)
10 small file cabinets and 3 large file cabinets; 136 cubic feet
D)
3 small file cabinets and 10 large file cabinets; 220 cubic feet
Solve.
59)
Greg is opening a car wash. He estimates his cost equation as C =8000 +0.08x and his revenue
equation as R =1.75x, where x is the number of cars washed in a six–month period. Find the
number of cars that must be washed in a six–month period for Greg to make a profit.
59)
A)
At least 47,905 cars
B)
At least 480 cars
C)
At least 4791 cars
D)
At least 3791 cars
Solve and graph the solution set on a number line.
60)
3(x + 1) +615
60)
A)
( , –6] [4, )
B)
[–8, 2]
C)
[–6, 4]
D)
( , –8] [2, )
D
Find the solution set for the equation.
61)
|7x – 1| =5
61)
A)
B)
–4
7
C)
–4
7, 6
7
D)
6
7
C
Find the intersection of the sets.
62)
{–5, –1, 2, 6}
{–3, 1, 5, 9}
62)
A)
{1}
B)
C)
{–5, –3, –1, 1, 2, 5, 6, 9}
D)
{–1, 1, 2}
B
C
Solve.
63)
An office manager buys two sizes of filing cabinets, small and large. Each small cabinet holds 3
cubic feet of files, and each large cabinet holds 15 cubic feet. Let x = the number of small file
cabinets bought and y = the number of large file cabinets bought. Write the objective function that
describes the total storage capacity of the file cabinets purchased.
63)
A)
z =15x +3y
B)
z =3x –15y
C)
z =15x –3y
D)
z =3x +15y
An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
64)
Objective Function z =9x + 9y
Constraints x 0
0 y 5
2x + 3y 12
2x + 3y 20
64)
A)
Maximum: 54; at (6, 0)
B)
Maximum: 90; at (10, 0)
C)
Maximum: 63; at (2, 5)
D)
Maximum: –36; at (4, 0)
Solve.
65)
Find the intersection: {–3, –1, 3, 4}
{3, 4, 9}.
65)
A)
{–3, –1, 3, 4, 9}
B)
{–3, –1, 3, 4}
C)
{3, 4}
D)
{3, 4, 9}
Graph the solution set of the system of inequalities or indicate that the system has no solution.
66)
2x – y –2
x + 3y 3
66)
35
A)
B)
C)
D)
Solve the linear inequality. Other than , graph the solution set on a number line.
67)
–3x –3(x – 7)
67)
A)
( , –7]
B)
[–7, )
C)
( , )
D)
Solve and graph the solution set on a number line.
68)
|x – 9| + 1 10
68)
A)
[0, 18]
B)
(–, 0) (18, )
C)
D)
(–, 0] [18, )
Find the solution set for the equation.
69)
|7x + 2| + 7 = – 2
69)
A)
–11
7, – 1
B)
–11
7
C)
1, 11
7
D)
D
37
D
Solve and graph the solution set on a number line.
70)
|x – 4| >6
70)
A)
[–2, 10]
B)
(–2, 10)
C)
D)
(–, –2) (10, )
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
71)
5x < – 5 and x +5>3
71)
A)
(–, –2) (–1, )
B)
[–2, –1]
C)
D)
(–2, –1)
38
Solve.
72)
Benjamin never has more than 23 hours free during the week. He is trying to make a weekly plan
for dividing his free time between reading and working out. He wants to spend at least 6 hours per
week reading. Write a system of inequalities to describe the situation. Let x represent the number of
hours for reading and y represent the number of hours for working out.
72)
A)
x + y 23, x 6, y 0
B)
x + y 23, x 6y, x
0, y 0
C)
x + y 23, x 6y, x
0, y 0
D)
x + y 23, y 6, x 0
Graph the inequality.
73)
5x + y > – 4
73)
A)
B)
C)
D)
39
Graph the solution set of the system of inequalities.
74)
x + 2y 8
4x – y 8
74)
A)
B)
C)
D)