Find the union of the sets.
67)
67)
{w, x, y, z, k}
A)
B)
{w, x, y, z, k}
C)
{w}
D)
{y, k}
Solve and graph the solution set on a number line.
68)
68)
|6x +
1| 6
A)
5
6,
B)
–7
6, 5
6
C)
, –7
65
6,
D)
–7
6, 5
6
Graph the solution set of the system of inequalities.
41
69)
2x – 3y –6
3x + 2y 12
x 0, y 0
69)
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.
70)
70)
–4x < – 4 and x +4>3
A)
(–, –1) (1, )
B)
(–1, 1)
C)
D)
(1, )
Solve the problem.
71)
71)
Given the cost function, C(x), and the revenue function, R(x), more than how many units must be
produced and sold for the business to make money?
C(x) =56x +3150
R(x) =77x
A)
more than 33 units
B)
more than 150 units
C)
more than 152 units
D)
more than 151 units
Find the solution set for the equation.
72)
72)
|6x + 5| + 6 =13
A)
2
5, –12
5
B)
C)
–1
3, 2
D)
1
3, – 2
Graph the inequality in a rectangular coordinate system.
43
73)
73)
3x + y 5
A)
B)
C)
D)
Graph the inequality.
44
74)
74)
x – y > – 6
A)
B)
C)
D)
Solve the inequality. Other than
, graph the solution set on a number line.
75)
75)
–2x 12
A)
[–6, )
B)
[6, )
C)
( , 6]
D)
( , –6]
Solve and graph the solution set on a number line. Express the solution set in both set–builder and interval notations.
76)
76)
|x + 3| < 0
A)
(–, –3)
B)
(3, )
C)
(–3, 3)
D)
46
Solve and graph the solution set on a number line.
77)
77)
x>1
A)
(–, –1) ( 1, )
B)
[–1, 1]
C)
(–1, 1)
D)
(–, –1] [1, )
Find the union of the sets.
78)
78)
{–5, –1, 2, 6}
{–4, 1, 5, 9}
A)
{–1, 1, 2}
B)
C)
{–5, –4, –1, 1, 2, 5, 6, 9}
D)
{1}
Solve the problem.
79)
79)
Greg is opening a car wash. He estimates his cost equation as C =8000 +0.08x and his revenue
equation as R =1.8x, 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.
A)
At least 466 cars
B)
At least 46,512 cars
C)
At least 4652 cars
D)
At least 3652 cars
47
80)
80)
It takes 19 minutes to set up a candy making machine. Once the machine is set up, it produces 10
candies per minute. Use an inequality to find the number of candies that can be produced in 8
hours if the machine has not yet been set up.
A)
4610 candies or fewer
B)
80 candies or fewer
C)
1520 candies or fewer
D)
8930 candies or fewer
Graph the inequality.
81)
81)
y 5
A)
B)
C)
D)
48
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.
82)
82)
–5x +
1 11 or 6x + 3 –21
A)
[–4, )
B)
[–4, –2]
C)
(–, )
D)
[–2,)
49
83)
83)
x <3 or x <7
A)
(–, 3)
B)
(3, 7)
C)
(–, 7)
D)
(–, 3)
(7, )
84)
84)
19 4x + 3 27
A)
(4, 6)
B)
(–, 4]
[6, )
C)
(–, 4)
(6, )
D)
[4, 6]
50
Solve.
85)
85)
The radius r of a plastic tube used in manufacturing a child’s toy must not differ from the
standard s by more than 3 millimeters. The manufacturing engineers express this as |r – s| 3. If
the standard s is 49, solve the inequality for the radius r. Express the answer in set–builder
notation.
A)
{ rr 46 or r 52 }
B)
{ r 43 r 46 }
C)
{ r 46 r 52 }
D)
{ r r 43 or r 46 }
86)
86)
The equation that represents the proper traffic control and emergency vehicle response
availability in a small city is 2P + 3F 23, where P is the number of police cars on active duty and
F is the number of fire trucks that have left the firehouse in response to a call. In order to comply
with staffing limitations, the equation 2P + F 17 is appropriate. The number of police cars on
active duty and the number of fire trucks that have left the firehouse in response to a call cannot
be negative, so P 0 and F 0. Graph the regions satisfying all the availability and staffing
requirements, using the horizontal axis for P and the vertical axis for F. If 5 police cars are on
active duty and 5 fire trucks have left the firehouse in response to a call, are all of the
requirements satisfied?
A)
Yes
B)
No
51
C)
Yes
D)
No
Solve and graph the solution set on a number line. Express the solution set in both set–builder and interval notations.
87)
87)
|x + 3| 0
A)
(–3, )
B)
(–3, 3)
C)
(–, )
D)
{–3}
52
Solve the problem.
88)
88)
Given the cost function, C(x), and the revenue function, R(x), more than how many units must be
produced and sold for the business to make money?
C(x) =13x +30,600
R(x) =30x
A)
more than 1801 units
B)
more than 652 units
C)
more than 1802 units
D)
more than 1800 units
Find the solution set for the equation.
89)
5x – 5
3=3
89)
A)
–14
5
B)
C)
14
5, –4
5
D)
4
5
Solve the problem.
90)
90)
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?
A)
25 or more rides
B)
22 or more rides
C)
24 or more rides
D)
23 or more rides
91)
91)
You invested $26,000 and started a business writing greeting cards. Supplies cost 11¢ per card
and you are selling each card for 75¢. Let x represent the number of cards produced and sold and
write the profit function, P. More than how many cards must be produced and sold for you to
make money?
A)
P(x) = 64x –26,000; more than 406 cards
B)
P(x) = 0.86x –26,000; more than 30,233 cards
C)
P(x) = 0.64x –26,000; more than 40,625 cards
D)
P(x) = 0.64x +26,000; more than 40,625 cards
Graph the inequality.
92)
92)
y x – 4
A)
B)
54
C)
D)
Solve the inequality. Other than
, graph the solution set on a number line.
93)
x
7–1
3x
4+3
93)
A)
–280
9,
B)
, –280
9
C)
–280
9,
D)
, –280
9
55
Solve and graph the solution set on a number line.
94)
94)
|x – 8| + 3 7
A)
(–, 4]
[12, )
B)
(–, 4)
(12, )
C)
D)
[4, 12]
Solve the problem.
95)
95)
When making a long distance call from a certain pay phone, the first three minutes of a call cost
$2.35. After that, each additional minute or portion of a minute of that call costs $0.35. Use an
inequality to find the number of minutes one can call long distance for $6.20.
A)
18 minutes or fewer
B)
3 minutes or fewer
C)
11 minutes or fewer
D)
14 minutes or fewer
Graph the solution set of the system of inequalities or indicate that the system has no solution.
96)
–2x + y <8
–2x + y >1
96)
56
A)
B)
C)
D)
Graph the inequality.
97)
x
4+y
2> 1
97)