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Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
115)
|x - 2| < 0
115)
A)
(-2, 2)
B)
C)
(-2, )
D)
(-, 2)
Find the solution set for the equation.
116)
3|x - 3| = 18
116)
A)
B)
{3, -9}
C)
{9, -3}
D)
{3}
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.
117)
-15 -4x + 5 < - 3
117)
A)
(2, 5]
B)
(-, 2] (5, )
C)
[2, 5)
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
118)
y < x
2x +7y >21
118)
A)
B)
62
C)
D)
119)
x 0
y 0
2x - 3y -6
3x + 2y
12
119)
A)
B)
63
C)
D)
Solve the problem.
120)
Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 5 hours to
make a hat and 2 hours to make an afghan, and she has no more than 40 hours available. She has
material for no more than 14 items and no more than 11 afghans. The bazaar will sell the hats for
$25 each and the afghans for $6 each. How many of each should she make to maximize the income
for the bazaar? What is the maximum income?
120)
A)
6 hats and 8 afghans; $198
B)
4 hats and 10 afghans; $160
C)
10 hats and 4 afghans; $274
D)
11 hats and 3 afghans; $293
Graph the inequality.
121)
y > x + 3
121)
64
A)
B)
C)
D)
Solve the problem.
122)
A doctor has told a patient to take vitamin pills. The patient needs at least 27 units of vitamin A, at
least 8 units of vitamin C, and at least 67 units of vitamin D. The red vitamin pills cost 20¢ each and
contain 6 units of A, 1 unit of C, and 4 units of D. The blue vitamin pills cost 40¢ each and contain 4
units of A, 1 unit of C, and 11 units of D. How many pills should the patient take each day to
minimize costs?
122)
A)
4 red and 4 blue
B)
8 red and 0 blue
C)
3 red and 5 blue
D)
5 red and 3 blue
Solve.
123)
A standard train ticket in a certain city costs $2.00 per ride. People who use the train also have the
option of purchasing a frequent-rider pass for $17.25 each month. With the pass, a ticket costs only
$1.25 per ride. How many train rides in a month make the frequent-rider pass a better deal than
standard train tickets?
123)
A)
23 or more rides
B)
25 or more rides
C)
24 or more rides
D)
22 or more rides
Solve and graph the solution set on a number line.
124)
5+1 -x
28
124)
A)
[-8, 4]
B)
(-, -8] [4, )
C)
(-, -4] [8, )
D)
[-4, 8]
Graph the inequality.
125)
x - y > - 3
125)
66
A)
B)
C)
D)
Write a system of three inequalities that describes the given constraints.
126)
An office manager is buying used filing cabinets. Small file cabinets cost $5 each and large file
cabinets cost $9 each, and the manager cannot spend more than $86 on file cabinets. A small cabinet
takes up 7 square feet of floor space and a large cabinet takes up 9 square feet, and the office has no
more than 106 square feet of floor space available for file cabinets. The manager must buy at least 7
file cabinets in order to get free delivery. Let x = the number of small file cabinets bought and y =
the number of large file cabinets bought.
126)
A)
5x +9y 86, 7x +9y 106, x + y 7
B)
5x +9y 86, 7x +9y 106, y 7
C)
5x +9y 86, 7x +9y 106, x + y 7
D)
5x +9y 86, 9x +7y 106, x 7
Graph the inequality.
67
127)
x + y < - 3
127)
A)
B)
C)
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
68
128)
x -1
y > - 5
128)
A)
B)
C)
D)
Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
129)
|3x - 3| - 2 > - 10
129)
A)
B)
-5
3, 11
3
C)
(-, )
D)
-5
3,
Find the value of the objective function at each corner of the graphed region. Use this information to answer the question.
130)
Objective Function z = x + 6y
What is the maximum value of the objective function?
130)
A)
16
B)
26
C)
21
D)
32
70
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.
131)
x 4 and x -1
131)
A)
(-, -1] [4, )
B)
C)
(-1, 4)
D)
[-1, 4]
Solve.
132)
It takes 21 minutes to set up a candy making machine. Once the machine is set up, it produces 20
candies per minute. Use an inequality to find the number of candies that can be produced in 5
hours if the machine has not yet been set up.
132)
A)
5580 candies or fewer
B)
100 candies or fewer
C)
2100 candies or fewer
D)
5880 candies or fewer
Solve. Use interval notation to express the range.
133)
On the first four exams, your grades are 76, 87, 64, and 77. You are hoping to earn a C in the course.
This will occur if the average of your five exam grades is greater than or equal to 70 and less than
80. What range of grades on the fifth exam will result in earning a C?
133)
A)
(46, 96]
B)
[46, 96)
C)
(36, 86]
D)
[36, 86)
Graph the inequality.
71
134)
x + 2y < - 2
134)
A)
B)
C)
D)
72
Find the intersection of the sets.
135)
{a, e, o, u}
135)
A)
{a}
B)
{a, e, o, u}
C)
D)
{u}
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.
136)
x 2 and x -1
136)
A)
(-, -1]
B)
[-1, 2]
C)
(-, -1] [2, )
D)
(-, 2]
Graph the inequality in a rectangular coordinate system.
137)
y > - 3
8x - 8
137)
73
A)
B)
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.
138)
-5x + 1 11 or 3x + 3 -9
138)
A)
(-, )
B)
[-4, )
C)
[-2,)
D)
[-4, -2]
Solve. Use interval notation to express the range.
139)
The formula for converting Fahrenheit temperature, F, to Celsius temperature, C, is
C =5
9(F - 32).
If Celsius temperature ranges from -95° to -30°, inclusive, what is the range for the Fahrenheit
temperature?
139)
A)
(-139, -22)
B)
[-28, -21]
C)
[-139, -22]
D)
(-28, -21)
Solve.
140)
A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however,
may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving
absolute value that expresses the relationship between the actual weight x of a bag and 40 pounds.
Solve the inequality, and express the answer in interval form.
140)
A)
|x|- 40 0.75 ; ( , 40.75]
B)
|40 - x| 0.75; [39.25, 40.75]
C)
|40 + x| 0.75; [39.25, 40.75]
D)
|x + 0.75| 40; [39.25, )
Solve the inequality. Other than , graph the solution set on a number line.
141)
-4(3x - 10) < - 16x + 16
141)
A)
[-6, )
B)
( , -6]
C)
(-6, )
D)
( , -6)
Graph the solution set of the system of inequalities.
142)
-1
y <10
142)
A)
B)
76
