31)
31)
x<1
A)
(–, –1] [1, )
B)
(–, –1) (1, )
C)
(–1, 1)
D)
[–1, 1]
Solve the problem.
32)
32)
Given the cost function, C(x), and the revenue function, R(x), write the profit function from
producing and selling x units of the product.
C(x) =8000x +40,000
R(x) =12,000x
A)
P(x) =4000x +40,000
B)
P(x) = – 4000x +40,000
C)
P(x) = – 4000x –40,000
D)
P(x) =4000x –40,000
Solve.
33)
33)
Marcus is planting a section of garden with tomatoes and cucumbers. The available area of the
section is 140 square feet. He wants the area planted with tomatoes to be more than 20% of the
area planted with cucumbers. Write a system of inequalities to describe the situation. Let x
represent the area (in square feet) planted in tomatoes and y represent the area (in square feet)
planted in cucumbers.
A)
x + y 140, x <0.20y, x 0, y 0
B)
x + y =140, x 0.20y, x 0, y 0
C)
x + y 140, x >20y, x 0, y 0
D)
x + y 140, x >0.20y, x 0, y 0
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.
34)
34)
x 2 or x 6
A)
(2, 6)
B)
[2, 6]
C)
D)
(–, 2] [6, )
Solve and graph the solution set on a number line.
35)
8+1 –x
210
35)
A)
(–, –6] [2, )
B)
(–, –2] [6, )
C)
[–2, 6]
D)
[–6, 2]
Graph the solution set of the system of inequalities.
22
36)
36)
–1 y <3
A)
B)
C)
D)
Graph the inequality.
23
37)
37)
x > – 4
A)
B)
C)
D)
Solve. Use interval notation to express the range.
38)
38)
The formula for converting Fahrenheit temperature, F, to Celsius temperature, C, is
C =5
9(F – 32).
If Celsius temperature ranges from –85° to –45°, inclusive, what is the range for the Fahrenheit
temperature?
A)
[–27, –23]
B)
(–27, –23)
C)
(–121, –49)
D)
[–121, –49]
Find the solution set for the equation.
39)
39)
|7x – 5| =2
A)
3
7, 1
B)
C)
3
7
D)
1
Solve the problem.
40)
40)
Claire has received scores of 85, 88, 87, and 80 on her algebra tests. What score must she receive
on the fifth test to have an overall test score average of at least 82?
A)
68 or greater
B)
71 or greater
C)
69 or greater
D)
70 or greater
Solve.
41)
41)
Find the union: {–3, –1, 3, 5} {3, 5, 7}.
A)
{–3, –1, 3, 5, 7}
B)
{3, 5, 7}
C)
{–3, –1, 3, 5}
D)
{3, 5}
Find the solution set for the equation.
42)
42)
|6x – 5| – 2 = – 5
A)
B)
1
3, –4
3
C)
4
3, –1
3
D)
1
3
Solve and graph the solution set on a number line.
43)
43)
|7x + 1| + 9 <13
A)
–, –5
7
B)
C)
–5
7, 3
7
D)
3
7, –5
7
Graph the solution set of the system of inequalities or indicate that the system has no solution.
26
44)
y 1
2 x 6
x – 2y –2
x + y
6
44)
A)
B)
C)
D)
Find the solution set for the equation.
45)
45)
|x + 8| =6
A)
B)
{–14, –2}
C)
{2}
D)
{14, –2}
46)
46)
|x – 8| = |9 – x|
A)
{17}
B)
1
2
C)
17
2
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.
47)
47)
x +6<4 and –6x < – 12
A)
(–2, 2)
B)
(–, –2) (2, )
C)
(–, –2)
D)
28
Solve the compound inequality. Other than
, graph the solution set on a number line.
48)
0 2x +1
2<4
48)
A)
–1
2, 7
2
B)
–1
2,7
2
C)
–1
2, 7
2
D)
–1
2,7
2
Graph the inequality.
49)
49)
y >2x – 5
29
A)
B)
C)
D)
Solve. Use interval notation to express the range.
50)
50)
Parts for an automobile repair cost $248. The mechanic charges $31 per hour. If you receive an
estimate for at least $341 and at most $403 for fixing the car, what is the time interval that the
mechanic will be working on the job?
A)
[11, 13]
B)
[1, 3]
C)
[3, 5]
D)
[1, 5]
Graph the inequality.
30
51)
51)
x + y < – 6
A)
B)
C)
D)
Solve.
52)
52)
The length
of a metal rod used in manufacturing cars must not differ from the standard s by
more than 0.5 inches. The manufacturing engineers express this as |– s| 0.5.If the standard s is
25.1, solve the inequality for the length
. Express the answer in set–builder notation.
A)
{ 24.6 or 25.6 }
B)
{ 24.6 25.6 }
C)
{ 25.6 26.1 }
D)
{ 25.6 or 26.1 }
Graph the solution set of the system of inequalities or indicate that the system has no solution.
53)
–x +3y <12
x 4
53)
A)
B)
32
C)
D)
Solve the inequality. Other than
, graph the solution set on a number line.
54)
54)
15x + 10 >5(2x + 10)
A)
(8, )
B)
( , 8)
C)
[8, )
D)
( , 8]
Graph the solution set of the system of inequalities or indicate that the system has no solution.
33
55)
y 2x – 4
y > – 2
3x
55)
A)
B)
C)
D)
Find the union of the sets.
56)
56)
{–5, –1, 1, 5} {1, 5, 9}
A)
{–5, –1, 1, 5, 9}
B)
{–5, –1, 1, 5}
C)
{1, 5}
D)
{1, 5, 9}
Solve the inequality. Other than
, graph the solution set on a number line.
57)
57)
3x – 7 2x – 12
A)
(–5, )
B)
(–, –5)
C)
[–5, )
D)
(–, –5]
35
Solve and graph the solution set on a number line.
58)
58)
3(x + 1) +618
A)
[–9, 3]
B)
(–7, 5)
C)
(–9, 3)
D)
[–7, 5]
59)
59)
|x + 8| >5
A)
(–, –13) (–3, )
B)
C)
(–13, –3)
D)
[–13, –3]
Solve. Use interval notation to express the range.
60)
60)
On the first four exams, your grades are 79, 91, 66, and 80. 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?
A)
(24, 74]
B)
(34, 84]
C)
[24, 74)
D)
[34, 84)
Solve the inequality. Other than
, graph the solution set on a number line.
61)
x
32+x
9
61)
A)
[9, )
B)
(–, 9]
C)
[–9, )
D)
(9, )
Graph the solution set of the system of inequalities or indicate that the system has no solution.
62)
3x – y 3
x + 4y –12
62)
37
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.
63)
63)
x –1 and x –3
A)
[–3, –1]
B)
(–3, –1)
C)
D)
(–, –3] [–1, )
Solve.
64)
64)
Chi is assigned to construct a triangle with the measure b of the base and the measure h of the
height differing by no more than 0.2 centimeters. Express the relationship between b and h as an
inequality involving absolute value.
A)
|h – b| > 0.2
B)
|b – h| < 0.2
C)
|b – h| 0.2
D)
|b + h| 0.2
Solve. Use interval notation to express the range.
65)
65)
On the first four exams, your grades are 75, 82, 67, and 76. 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?
A)
[60, 90]
B)
[50, 100]
C)
[60, 90)
D)
[50, 100)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
39
66)
66)
–1 y <6
A)
B)
C)
D)