Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
For the compound inequality, give the solution set in both interval and graph forms.
1)
6x + 10 -2 or 6x + 10 22
1)
A)
[-2, )
B)
(–, -2] [2, )
C)
[-2, 2]
D)
(–, 2]
1
Solve and graph. Write the solution in interval notation.
2)
4.2 – 4
5w<5.4
2)
A)
– 51
20 , 219
20
B)
–, – 3
212,
C)
– 3
2, 12
D)
– 3
2,
Graph the compound inequality.
3)
x 0and x <4
3)
A)
B)
C)
D)
Solve.
4)
46.5% of the students at a certain college are men. If the total number of students at the college is
3400, how many female students are there?
4)
A)
1839 students
B)
1700 students
C)
1581 students
D)
1819 students
2
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
5)
-11a– 8 -12a– 17
5)
A)
{a a <-11}; ( , -11)
B)
{a a >-11}; (-11, )
C)
{a a -9}; ( ,-9]
D)
{a a -9}; [-9, )
Solve by separating the two absolute values into equal and opposite cases.
6)
1
2n + 2 =3
4n – 2
6)
A)
{16, 0}
B)
{16, 12}
C)
{0}
D)
Solve the inequality. Give the solution set in both set–builder notation and graph form.
7)
8x – 10 <-2 and -1 – 4x >-13
7)
A)
x 1 < x < 3
B)
x x < 1 or x > 3
C)
x x < 1
D)
x x < 3
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
8)
-5y+ 2 >-6y+ 3
8)
A)
{y y <1}; ( ,1)
B)
{y y >5}; (5, )
C)
{ y y >1}; (1, )
D)
{y y <5}; ( , 5)
3
Solve by separating the two absolute values into equal and opposite cases.
9)
4 – 5z =3z – 6
9)
A)
-5, 5
4
B)
-1, – 1
4
C)
-1, 5
4
D)
5
4
Solve the problem.
10)
In order for a chemical reaction to remain stable, its Celsius temperature must be no more than
117.6°C. Find the Fahrenheit temperatures at which the reaction will remain stable. (F = 9
5C + 32)
10)
A)
F 47.56°
B)
F 243.68°
C)
F 243.68°
D)
F 47.56°
Write an inequality involving absolute value that describes the graph shown.
11)
11)
A)
x <8
B)
x – 8> 0
C)
x >8
D)
x – 8< 0
Solve the inequality. Give the solution set in both interval and graph forms.
12)
x –1<3 and x +31
12)
A)
(–, -2](4, )
B)
(–, 4)
C)
[-2, )
D)
[-2, 4)
4
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
13)
4n – 10 >3n + 2
13)
A)
{n n >12}; (12, )
B)
{n n <12}; ( , 12)
C)
{n n –8}; ( , –8]
D)
{n n –8}; [–8, )
Solve and check.
14)
2m –6=12 +16
14)
A)
40
B)
19
C)
68
D)
17
Solve the equation for the indicated variable.
15)
S = 2rh + 2r2; solve for h
15)
A)
h = S – r
B)
h = 2(S – r)
C)
h =S – 2r2
2r
D)
h =S
2r– 1
Graph the compound inequality.
16)
-4 x <0
16)
A)
B)
C)
D)
Use the formula B = P + Prt, which is used to calculate the balance in an account if simple interest is added to a principal P
at an interest rate of r for t years.
17)
Suppose that an account earns 4.7% interest and after two years the balance is $4055.00. Find the
principal that was invested.
17)
A)
$4475.72
B)
$4447.90
C)
$3335.92
D)
$3706.58
5
Solve by separating the two absolute values into equal and opposite cases.
18)
3s – 5 = s + 2
18)
A)
– 7
2, – 3
2
B)
7
2, 3
4
C)
D)
7
2, – 6
Solve and graph. Write the solution in interval notation.
19)
b + 9 – 9 1
19)
A)
(–, -19] [1, )
B)
[17, 19]
C)
[-19, 1]
D)
(–, -19] [-17, )
Solve the equation.
20)
3z – 4
3–2
3= 6
20)
A)
– 16
3, 8
B)
– 8
3, 16
9
C)
8
3
D)
– 16
9, 8
3
Solve by isolating the absolute value and using the absolute value property.
21)
k+ 2 =12
21)
A)
{-10}
B)
{10}
C)
{14, -14}
D)
{10, -10}
Translate the sentence to an inequality.
22)
A number is greater than 8.
22)
A)
x 8
B)
x >8
C)
x <8
D)
x 8
Write an inequality involving absolute value that describes the graph shown.
23)
23)
A)
x >8
B)
x + 2 <8
C)
x + 2 >8
D)
x <8
6
Solve the problem.
24)
In order for a chemical reaction to remain stable, its Celsius temperature must be 79.16°C. Find the
Fahrenheit temperature at which the reaction will remain stable. (C = 5
9(F – 32))
24)
A)
192.34°F
B)
26.2°F
C)
174.49°F
D)
92.38°F
Solve the equation for the indicated variable.
25)
V =14s3; solve for s3
25)
A)
s3=14V
B)
s3= V –14
C)
s3=14
V
D)
s3=V
14
Solve and graph. Write the solution in interval notation.
26)
2k + 3 – 7 <-5
26)
A)
B)
–, –1
2
C)
– 5
2, –1
2
D)
–, – 5
2–1
2,
7
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
27)
12n + 12 2(5n + 9)
27)
A)
{n n >3}; (3, )
B)
{n n 3}; [3, )
C)
{n n <3}; ( , 3)
D)
{n n 3}; ( , 3]
Solve by isolating the absolute value and using the absolute value property.
28)
14 –3 4 + 7z=-5
28)
A)
1
3, – 31
21
B)
1
3
C)
5
7, – 23
21
D)
1, – 31
7
Solve and graph. Write the solution in interval notation.
29)
5– 2x8
29)
A)
– 3
2, 13
2
B)
– 13
2, 3
2
C)
D)
–, – 3
213
2,
8
Solve the problem.
30)
If the formula R = –0.037t + 50.1 can be used to predict the world record in the 400-meter dash
t years after 1925, for what years will the world records be 47.9 seconds or less?
30)
A)
t 1984
B)
t 1985
C)
t >1986
D)
t >1960
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
31)
–2x <– 2
7
31)
A)
xx < 0; , 0
B)
xx > 0; 0,
C)
xx > 1
7; 1
7,
D)
xx < – 1
7; , – 1
7
Solve and check. Note that the equation could be an identity or a contradiction.
32)
6r –40 –16r =-45 + r
32)
A)
5
9
B)
– 85
9
C)
– 85
11
D)
5
11
9
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
33)
–5>x
-5
33)
A)
{x x 25}; [25, )
B)
{x x 25}; ( , 25]
C)
{x x >25}; (25, )
D)
{x x <25}; ( , 25)
Solve the problem.
34)
Charlie needs to make a rectangular cover for a sandbox. It needs to cover at least 49 square feet.
The width is 7 feet. What range of values can the length have?
34)
A)
8 feet or more
B)
7 feet or more
C)
6 feet or less
D)
42 feet or more
Solve and check. Note that the equation could be an identity or a contradiction.
35)
0.8(5x + 15) =2.7 – (x + 3)
35)
A)
5
B)
– 123
50
C)
3
10
D)
– 120
41
Translate the sentence to an inequality.
36)
A number is less than or equal to –2.
36)
A)
x –2
B)
x –2
C)
x < –2
D)
x > –2
37)
Two times a number less than twenty–seven must be more than fifty.
37)
A)
2x –27 50
B)
27 –2x >50
C)
2x –27 <50
D)
2(x –27) 50
10
Write the inequality in set–builder notation, interval notation, and then graph the solution set.
38)
x <4
38)
A)
{x |x <4 } ; (–, 4);
B)
{x |x 4 } ; (–, 4];
C)
{x |x 4 } ; [4, );
D)
{x |x >4 } ; (4, );
Solve by isolating the absolute value and using the absolute value property.
39)
2–2k + 3 =-7
39)
A)
– 6
B)
3
C)
– 6, 3
D)
– 3, 6
Solve the inequality. Give the solution set in both set–builder notation and graph form.
40)
x –1>2 or x +2<3
40)
A)
x x < 1 or x > 3
B)
x x < –1 or x > 3
C)
x x > 1
D)
x x < 3
Solve and check. Note that the equation could be an identity or a contradiction.
41)
8(p +6) –6p – 24 =24 +2p
41)
A)
12
B)
0
C)
All real numbers
D)
No solution
11
Solve the inequality. Give the solution set in both interval and graph forms.
42)
0<5y 20
42)
A)
(0, 4)
B)
(0, 4]
C)
[0, 4]
D)
[0, 4)
Solve using the absolute value property.
43)
2x – 4 =7
43)
A)
11
2
B)
–3
2, 11
2
C)
– 11
2, 3
2
D)
– 11
2
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
44)
0.6x +15 + x > 2x +19 – 0.5x
44)
A)
{x x -4}; [-4, )
B)
{x x <-4}; ( ,-4)
C)
{x x >40}; (40, )
D)
{x x <40}; ( ,40)
12
Solve the inequality. Give the solution set in both set–builder notation and graph form.
45)
9x – 6 <3x or -4x -12
45)
A)
x x < 1 or x 3
B)
x 1 < x 3
C)
D)
x x is a real number
Solve and graph. Write the solution in interval notation.
46)
3– y + 2–10
46)
A)
(–, 11)
B)
[-13, 13]
C)
(–, -15] [11, )
D)
[-15, 11]
13
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
47)
-4m – 8 -5m + 2
47)
A)
{m m <-4}; ( , -4)
B)
{m m 10}; ( , 10]
C)
{m m >-4}; (-4, )
D)
{m m 10}; [10, )
Solve the problem.
48)
Suppose that the sales of a particular brand of appliance satisfy the relationship S(x) = 190x + 1800,
where S(x) represents the number of sales in year x, with x = 0 corresponding to 1990. For what
years will sales be between 2940 and 3700?
48)
A)
Between 7 and 11
B)
Between 1996 and 1999
C)
Between 1995 and 1999
D)
Between 1996 and 2000
Solve and graph. Write the solution in interval notation.
49)
6x + 8 <1
49)
A)
–, – 3
2– 7
6,
B)
– 3
2, – 7
6
C)
–, – 3
2
D)
(–, 6)
14
Solve and check.
50)
2x –2=16
50)
A)
9
B)
18
C)
36
D)
20
Find the indicated intersection or union.
51)
{4, 8, 12, 16} {3, 6, 9, 12}
51)
A)
{3, 4, 8, 9, 12, 16}
B)
{12}
C)
{3, 4, 6, 8, 9, 12, 12, 16}
D)
{3, 4, 6, 8, 9, 12, 16}
Solve the inequality. Give the solution set in both set–builder notation and graph form.
52)
36x + 9 and 2x + 4 <10
52)
A)
x -1 x 3
B)
x -1 < x 3
C)
x -1 x < 3
D)
x -1 < x < 3
Write the inequality in set–builder notation, interval notation, and then graph the solution set.
53)
x 5
53)
A)
{x |x <5} ; (–, 5);
B)
{x |x 5} ; [2, ];
C)
{x |x 5} ; (–, 5];
D)
{x |x >5} ; (2, ];
15
Write an inequality involving absolute value that describes the graph shown.
54)
54)
A)
x – 6 < 2
B)
x – 3 > 2
C)
x + 3 > 2
D)
x > –6
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
55)
x – 5
21 >– 20
21
55)
A)
xx < – 4
7; , – 4
7
B)
xx > 5
7; 5
7,
C)
xx > – 5
7; – 5
7,
D)
xx > – 5
7; – 5
7,
16
Solve and graph. Write the solution in interval notation.
56)
x >4
56)
A)
(-4, 4)
B)
(4, )
C)
(-4, )
D)
(–, -4) (4, )
Solve the inequality. Give the solution set in both interval and graph forms.
57)
9x + 4 31 and 7x – 3 25
57)
A)
(–, 3] [4, )
B)
[3, )
C)
[4, )
D)
[3, 4]
17
Solve and graph. Write the solution in interval notation.
58)
7 – 4x
73
58)
A)
– 7
2, 7
B)
–, – 7
27,
C)
D)
– 7
2,
Solve.
59)
A bookstore determines the retail price by marking up the wholesale price 25%. The retail price of
a physics book is $114.75. What was the wholesale price?
59)
A)
$86.06
B)
$91.80
C)
$143.44
D)
$66.80
Solve the problem.
60)
Find the range (to the nearest tenth) of values for the Fahrenheit temperature when the Celsius
temperature ranges between 4°C and 8°C, inclusive. (Use the formula F = 9
5C + 32.)
60)
A)
Between 34.2°F and 32.8°F, inclusive
B)
Between 7.2°F and 14.4°F, inclusive
C)
Between 23.2°F and 30.4°F, inclusive
D)
Between 39.2°F and 46.4°F, inclusive
18
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
61)
-4(2y + 10) <-12y – 36
61)
A)
{y y 1}; ( , 1]
B)
{y y 1}; [ 1, )
C)
{y y <1}; ( , 1)
D)
{y y >1}; ( 1, )
Write an inequality involving absolute value that describes the graph shown.
62)
62)
A)
x + 3 2
B)
x –6
C)
x – 6 2
D)
x – 3 2
For the compound inequality, give the solution set in both interval and graph forms.
63)
12x – 8 <4x or -2x -6
63)
A)
(1, 3]
B)
(–, 1) [3, )
C)
(–, )
D)
19
Graph the compound inequality.
64)
-6 < x < –2
64)
A)
B)
C)
D)
Solve using the absolute value property.
65)
6m + 2 = –8
65)
A)
– 5
3
B)
– 1, 5
3
C)
D)
1, – 5
3
Solve the inequality. Give the solution set in both interval and graph forms.
66)
-12 <-4a4
66)
A)
[-3, 1)
B)
[-1, 3)
C)
(-1, 3]
D)
(-3, 1]
Solve.
67)
Two cars leave a parking lot and travel in opposite directions. One travels at 10 miles per hour and
the other travels at 7 miles per hour. In how many hours will the two cars be 68 miles apart?
67)
A)
4 hr.
B)
8 hr.
C)
12 hr.
D)
9 hr.
Solve using the absolute value property.
68)
3m + 4 =8
68)
A)
4
3
B)
4
3, – 4
C)
– 4
3, 4
D)
1, – 3
20
Solve the inequality. Give the solution set in both set–builder notation and graph form.
69)
4< 1 – 4x 8
69)
A)
x – 7
4< x 3
4
B)
x – 7
4 x < – 3
4
C)
x – 7
4< x – 3
4
D)
x – 7
4 x < 3
4
Solve and graph. Write the solution in interval notation.
70)
3x – 7 3
70)
A)
4
3, 10
3
B)
–, – 10
3– 4
3,
C)
10
3,
D)
–, 4
310
3,
21
Solve the inequality. Give the solution set in both set–builder notation and graph form.
71)
–5x + 1 11 or 3x + 3 -9
71)
A)
x x -4
B)
x x is a real number
C)
x –4 x -2
D)
x x -2
Solve and graph. Write the solution in interval notation.
72)
r + 4 >9
72)
A)
(5, )
B)
C)
(–, -13) (5, )
D)
(-13, 5)
Solve the equation.
73)
-8x + 7
-8 =-5
73)
A)
-33
-8 , -43
-8
B)
-47
-8 , -33
-8
C)
D)
-47
-8 , 33
-8
22
Solve and graph. Write the solution in interval notation.
74)
4 x – 1 <1
74)
A)
–, 3
45
4,
B)
– 5
4, – 3
4
C)
–, – 5
4– 3
4,
D)
3
4, 5
4
Write an inequality involving absolute value that describes the graph shown.
75)
75)
A)
x – 8 0
B)
x 8
C)
x 8
D)
x – 8 0
Solve the inequality. Give the solution set in both set–builder notation and graph form.
76)
–4<2x 4
76)
A)
x –2< x < 2
B)
x –2 x 2
C)
x –2 x < 2
D)
x –2< x 2
Solve the equation for the indicated variable.
77)
P = 2L + 2W; solve for L
77)
A)
L=P – 2W
2
B)
L= P –W
C)
L= d – 2W
D)
L=P – W
2
23
Solve using the absolute value property.
78)
8 – (3 – y) = 14
78)
A)
{–9}
B)
{–9, 19}
C)
{9}
D)
{–19, 9}
Solve and graph. Write the solution in interval notation.
79)
g – 2 <8
79)
A)
(-6, )
B)
(-6, 10)
C)
D)
(–, 10)
Write an inequality involving absolute value that describes the graph shown.
80)
80)
A)
x – 3 2
B)
x –6
C)
x + 3 2
D)
x – 6 2
24
Solve and graph. Write the solution in interval notation.
81)
3y + 1 – 7 >-10
81)
A)
–, – 4
32
3,
B)
C)
– 4
3,
D)
(–, )
Solve and check. Note that the equation could be an identity or a contradiction.
82)
3(q – 3) +4q – 1 =4q + 5 +3q
82)
A)
3
B)
4
C)
All real numbers
D)
No solution
Solve the inequality. Give the solution set in both set–builder notation and graph form.
83)
-4x+ 2 >-14 or -4x+ 2 2
83)
A)
x x is a real number
B)
x x 0
C)
x x 0 or x > 4
D)
x x < 4
25
Graph the inequality.
84)
x 2 or x 6
84)
A)
B)
C)
D)
Solve by separating the two absolute values into equal and opposite cases.
85)
4s – 9 = s + 5
85)
A)
B)
14
3
C)
– 14
3, – 4
5
D)
14
3, 4
5
Write the inequality in set–builder notation, interval notation, and then graph the solution set.
86)
x >-6
86)
A)
{x |x -6 } ; (–, -6];
B)
{x |x >-6 } ; (-6, );
C)
{x |x -6 } ; [-6, );
D)
{x |x <-6 } ; (–, -6);
Translate the sentence to an inequality.
87)
Two added to half of a number is at most seven.
87)
A)
1
2x +27
B)
1
2x +2>7
C)
1
2x +2<7
D)
1
2x +27
For the compound inequality, give the solution set in both interval and graph forms.
88)
x >3 or x 5
88)
A)
(3, )
B)
(3, 5]
C)
(–, 3) [5,)
D)
(–, )
26
Write the inequality without “and”.
89)
x >-4 and x 0
89)
A)
-4 < x 0
B)
-4 > x 0
C)
-4 x <0
D)
0 x <-4
Solve and graph. Write the solution in interval notation.
90)
3z – 3 +214
90)
A)
–, – 1 7,
B)
– 1, 7
C)
7,
D)
–, – 4 4,
Solve.
91)
Twenty–seven less than eight times a number is equal to five. What is the number?
91)
A)
4
B)
–1
C)
11
4
D)
–4
27
Solve and graph. Write the solution in interval notation.
92)
3– 9x6
92)
A)
– 1, 1
3
B)
– 1
3, 1
C)
–, – 1
31,
D)
–, – 1 1
3,
Write the inequality in set–builder notation, interval notation, and then graph the solution set.
93)
x -4
93)
A)
{x |x <-4} ; (–, -4);
B)
{x |x >-4} ; (-4, );
C)
{x |x -4} ; [-4, );
D)
{x |x -4} ; (–, -4];
Solve and check. Note that the equation could be an identity or a contradiction.
94)
5m +7+5(2m –4) –4(m +4) = 0
94)
A)
29
11
B)
3
11
C)
43
11
D)
29
19
28
Solve the problem.
95)
A yoga studio is being designed in the shape of a trapezoid. The lengths of the two parallel sides
are 56 feet and 44 feet. The area of the studio is to be at least 1600 square feet and not more than
2000 square feet. What is the range of possible values for the width of the studio?
[Hint: the area of a trapezoid is A =1
2w(a + b) where a and b are the lengths of the two parallel
sides.]
95)
A)
w 64 ft w 80 ft
B)
w 17 ft w 35 ft
C)
w 32 ft w 40 ft
D)
w w 32 ft
Solve and graph. Write the solution in interval notation.
96)
3 x +7>23
96)
A)
(–, – 2
3) (2
3, )
B)
(16
3, )
C)
(2
3, )
D)
(–, – 16
3) (16
3, )
Graph the compound inequality.
97)
-1 x 3
97)
A)
B)
C)
D)
29
98)
x >-6 and x –2
98)
A)
B)
C)
D)
Solve.
99)
Two trains traveling on parallel tracks are going toward each other from a distance of 600
kilometers. If one train is moving at 50 kilometers per hour and the other is moving at
100kilometers per hour, after how many hours will the trains pass each other?
99)
A)
1 hr.
B)
5 hr.
C)
6 hr.
D)
4 hr.
Solve and check. Note that the equation could be an identity or a contradiction.
100)
1
3(r + 6) =1
6(r + 8)
100)
A)
4
B)
-12
C)
3
D)
-4
Solve and check.
101)
6p +2=7p –2
101)
A)
2
B)
6
C)
0
D)
4
Solve by separating the two absolute values into equal and opposite cases.
102)
n – 9 =4 – n
102)
A)
13
2
B)
–5
2
C)
{13}
D)
30
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
103)
6x – 2 >2(2x – 4)
103)
A)
{x x –3}; [–3, )
B)
{x x –3}; ( ,–3]
C)
{x x < –3}; ( ,–3)
D)
{x x > –3}; (–3, )
Solve and check.
104)
9– 4u =3
104)
A)
3
2
B)
– 3
2
C)
-6
D)
6
Graph the compound inequality.
105)
x >-3 and x <1
105)
A)
B)
C)
D)
Find the indicated intersection or union.
106)
{4, 8, 12, 16} {3, 6, 9}
106)
A)
{3, 4, 6, 8, 9, 12, 16}
B)
{0}
C)
{4, 8, 12, 16}
D)
31
Graph the inequality.
107)
x >2 or x 5
107)
A)
B)
C)
D)
Solve and check.
108)
5x +5(4x –5) =3
108)
A)
1
B)
28
25
C)
22
25
D)
3
25
Solve by isolating the absolute value and using the absolute value property.
109)
8m + 6 + 2 =9
109)
A)
– 1
8, 13
8
B)
1
8, – 13
8
C)
D)
1
6, – 13
6
Find the indicated intersection or union.
110)
{q, s, u, v, w, x}
110)
A)
{q}
B)
{q, s, u, v, w, x}
C)
D)
{q, s, u, v, w}
Solve the equation for the indicated variable.
111)
A =1
2bh; solve for b
111)
A)
b =h
2A
B)
b =2A
h
C)
b =A
2h
D)
b =Ah
2
Solve by isolating the absolute value and using the absolute value property.
112)
b + 5 + 5 =13
112)
A)
{-3, 13}
B)
{3}
C)
D)
{3, -13}
Solve.
113)
A hardware store had monthly sales of $53,800 and spent 28% of it on health insurance. How much
was spent on health insurance?
113)
A)
$150,640
B)
$15,064
C)
$19,214
D)
$192,143
Solve the problem.
114)
Raymond plans on playing 5 rounds of golf while on vacation. He wants his average to be 90 or
less. His scores for the first 4 rounds were 88, 92, 89, and 89. What does he need to score on the last
round to meet his goal?
114)
A)
88 or less
B)
82 or less
C)
90 or more
D)
92 or less
Solve.
115)
The product of negative three and a number is forty–eight. What is the number?
115)
A)
-16
B)
51
C)
16
D)
3
32
Solve and graph. Write the solution in interval notation.
116)
3 x +4<13
116)
A)
– 3 , 3
B)
1
3 , – 1
3
C)
–, 1
3
D)
–, 3
Find the indicated intersection or union.
117)
{v, w, x, y, z} {q, s, y, z}
117)
A)
{s, u, w}
B)
{q, s, v, w, x, y, z}
C)
{q, s, u, v, w, x, y}
D)
{s, u, v, w, x, z}
For the compound inequality, give the solution set in both interval and graph forms.
118)
x –1>1 or x +1<2
118)
A)
(–, 1)(2, )
B)
(1, )
C)
(–, 2)
D)
(–, -1)(2, )
Solve.
119)
A chemical solution contains 9% calcium. How much calcium is in 2 mL of solution?
119)
A)
0.18 mL
B)
1.8 mL
C)
22.222 mL
D)
2.222 mL
33
120)
Twenty–nine minus eight times a number is equal to five. What is the number?
120)
A)
3
B)
–3
4
C)
–3
D)
3
4
Solve by separating the two absolute values into equal and opposite cases.
121)
n – 5 =1 – n
121)
A)
3
B)
{6}
C)
– 2
D)
Solve the problem.
122)
Anita receives a promotional offer from a long–distance phone company of $0.03 per minute for
long–distance calls. If she spends between $6 and $18 on long distance calls in the first month, the
offer will be extended by an extra month. If she spends more than $18 in the first month, the offer
will be extended by an additional two months. For what range of minutes must Anita use long
distance in the first month, if the offer is to be extended by an extra month?
122)
A)
x 100 min x 600 min
B)
x x 200 min
C)
x 200 min x 600 min
D)
x 200 min x 900 min
Solve using the absolute value property.
123)
b – 4 =7
123)
A)
B)
{11, -3}
C)
{11}
D)
{-11, 3}
Find the indicated intersection or union.
124)
{q, s, u, v, w, x, y, z}
{s}
124)
A)
{q, s, u, v, w, x, y}
B)
{s}
C)
{v, x}
D)
{s, u, w}
Solve the problem.
125)
Assume that the mathematical model C(x) =19x +170 represents the cost C, in hundreds of dollars,
for a certain manufacturer to produce x items. How many items x can be manufactured if the cost is
to be kept between $739,000 and $1,100,000?
125)
A)
{x 400< x <600}
B)
{x 380< x <570}
C)
{x 570< x <760}
D)
{x 600< x <800}
Solve.
126)
A number increased by seven is negative twelve. What is the number?
126)
A)
-5
B)
19
C)
7
D)
-19
34
Solve and graph. Write the solution in interval notation.
127)
7 – 2x
73
127)
A)
–, – 7 14,
B)
(–, )
C)
– 7,
D)
– 7, 14
128)
0.25z – 5+1>3
128)
A)
28,
B)
–, 12 28,
C)
12, 28
D)
–, -28 28,
35
129)
x 16
129)
A)
(–, -16]
B)
(–, -16] [16, )
C)
(–, 16]
D)
[-16, 16]
Solve and check. Note that the equation could be an identity or a contradiction.
130)
12n +2(n – 3) =11 + 5(2n – 1)
130)
A)
11
2
B)
3
C)
6
D)
– 5
2
Solve by separating the two absolute values into equal and opposite cases.
131)
3s – 7 = 7 – 3s
131)
A)
all real–number solutions
B)
7
3
C)
– 7
3, 7
3
D)
36
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
132)
a
-4 <4
132)
A)
{a a >-16}; (-16, )
B)
{a a -16}; [-16, )
C)
{a a -16}; ( , -16]
D)
{a a <-16}; ( , -16)
Solve the inequality. Give the solution set in both set–builder notation and graph form.
133)
-2y+ 3 <9 or -2y+ 3 17
133)
A)
y y < -3
B)
y3< y 7
C)
y y -7 or y > -3
D)
y y -7
134)
-21 <-4x + 3 –5
134)
A)
x 2< x 6
B)
x -6 < x –2
C)
x 2 x < 6
D)
x -6 x < –2
Solve using the absolute value property.
135)
9– 5x=1
135)
A)
– 2, – 8
5
B)
8
5, 2
C)
– 2
D)
8
5
37
Solve the equation for the indicated variable.
136)
F =9
5C + 32; solve for C
136)
A)
C =9
5(F – 32)
B)
C =F – 32
9
C)
C =5
F – 32
D)
C =5
9(F – 32)
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
137)
a – 10 <-21
137)
A)
{a a >-11}; (-11, )
B)
{a a -11}; [-11, )
C)
{a a -11}; ( , -11]
D)
{a a <-11}; ( , -11)
Translate the sentence to an inequality.
138)
Negative five is greater than sixty less than nine times a number.
138)
A)
–5>60 –9x
B)
–5+60 9x
C)
–5+60 <9x
D)
–5>9x –60
Write an inequality involving absolute value that describes the graph shown.
139)
139)
A)
x – 3 > 2
B)
x < –6
C)
x – 6 < 2
D)
x + 3 < 2
140)
140)
A)
x <2
B)
x – 2> 0
C)
x >2
D)
x – 2< 0
Solve.
141)
If two less than a number is fourteen, what is the number?
141)
A)
16
B)
12
C)
2
D)
-12
Solve the problem.
142)
A one–story building is 280 ft by 200 ft. If a square patio with sides 16 ft occupies the center of the
building, how much area remains for offices?
142)
A)
944 ft2
B)
960 ft2
C)
896 ft2
D)
55,744 ft2
38
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
143)
x + 1 <12
143)
A)
{x x 11}; ( , 11]
B)
{x x 11}; [11, )
C)
{x x >11}; (11, )
D)
{x x <11}; ( , 11)
For the compound inequality, give the solution set in both interval and graph forms.
144)
8x + 9 1or 8x + 9 33
144)
A)
(–, -1] [3, )
B)
[-1, )
C)
[-1, 3]
D)
(–, 3]
Solve by isolating the absolute value and using the absolute value property.
145)
3–5z + 1 =-5
145)
A)
3
5
B)
– 13
5, 3
5
C)
– 3
5, 13
5
D)
– 9
5, 7
5
Translate the sentence to an inequality.
146)
Two times a number less twenty–six must be more than sixty.
146)
A)
2x –26 60
B)
2(x –26) 60
C)
2x –26 >60
D)
2(x –26) >60
39
Solve the inequality. Give the solution set in both interval and graph forms.
147)
–14 4x + 2 and 6x – 9 < –9
147)
A)
(-4, 0)
B)
[-4, 0]
C)
(-4, 0]
D)
[-4, 0)
148)
-3 <-2a+ 5 5
148)
A)
[-4, 0)
B)
(0, 4]
C)
(-4, 0]
D)
[0, 4)
Graph the inequality.
149)
x <2 or x <7
149)
A)
B)
C)
D)
Solve and check.
150)
8q –3=4q +9
150)
A)
16
B)
3
C)
5
D)
9
40
Solve the inequality. Give the solution set in both set–builder notation and graph form.
151)
-16 <4x – 4 and 2x + 7 <9
151)
A)
x -3 x < 1
B)
x -3 x 1
C)
x -3 < x 1
D)
x -3 < x < 1
152)
6x + 6 -18 or 6x + 6 6
152)
A)
x x -4 or x 0
B)
x x -4
C)
x x 0
D)
x -4 x 0
Write an inequality involving absolute value that describes the graph shown.
153)
153)
A)
x 3
B)
x 3
C)
x – 3 0
D)
x – 3 0
41
For the compound inequality, give the solution set in both interval and graph forms.
154)
x <5 or x <7
154)
A)
(–, 7)
B)
(5, )
C)
(–, 5) (7, )
D)
(5, 7)
Solve and graph. Write the solution in interval notation.
155)
5 3z – 3+220
155)
A)
–, – 1
511
5,
B)
– 1
5, 11
5
C)
–, 11
5
D)
– 6
5, 6
5
42
Solve the equation.
156)
–3– 7x
7=2
156)
A)
-17
7, 11
7
B)
-11
7, 13
7
C)
D)
7
-17, 7
11
Solve the inequality. Give the solution set in both set–builder notation and graph form.
157)
5x + 21 -35 or 5x + 21 35
157)
A)
xx – 56
5 or x 14
5
B)
xx – 56
5
C)
xx is a real number
D)
xx -12 or x 2
Solve and graph. Write the solution in interval notation.
158)
–5x – 1 <8
158)
A)
– 9
5, 7
5
B)
–, – 9
5
C)
(–, 5)
D)
–, – 9
57
5,
43
For the compound inequality, give the solution set in both interval and graph forms.
159)
x 3 or x 5
159)
A)
(-3, 5)
B)
(–, 3] [5,)
C)
(–, 5]
D)
[3, 5]
Solve and graph. Write the solution in interval notation.
160)
7 – x 12
160)
A)
[-5, 19]
B)
(–, 19]
C)
(–, -5]
D)
(–, -5] [19, )
Solve the equation for the indicated variable.
161)
A = P(1 + nr); solve for r
161)
A)
r =A
n
B)
r =P – A
Pn
C)
r =A – P
Pn
D)
r =Pn
A – P
44
Solve the inequality. Give the solution set in both set–builder notation and graph form.
162)
-22 6x – 4 2
162)
A)
x -3 < x 1
B)
x -3 x < 1
C)
x -3 x 1
D)
x -3 < x < 1
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
163)
2
3(2x – 1) <6
163)
A)
{x x <– 5}; ( ,– 5)
B)
{x x 5}; ( ,5]
C)
{x x <5}; ( ,5)
D)
{x x – 5}; [– 5, )
45
For the compound inequality, give the solution set in both interval and graph forms.
164)
-2z+ 4 <4 or -2z+ 4 12
164)
A)
(0, 4]
B)
[-4, )
C)
(–, 0)
D)
(–, -4] (0, )
Graph the compound inequality.
165)
x 2 and x –3
165)
A)
B)
C)
D)
Solve by isolating the absolute value and using the absolute value property.
166)
4 8x – 10 – 8 = –6
166)
A)
21
16
B)
33
16
C)
19
16, 21
16
D)
7
16 , 33
16
Solve and check.
167)
3x +6=21
167)
A)
5
B)
45
C)
15
D)
27
Solve the equation.
168)
5 + 1
8x=4
168)
A)
[72, -8}
B)
{-72, -8}
C)
D)
{8, 72}
46
Solve and graph. Write the solution in interval notation.
169)
b – 9 – 3 9
169)
A)
[-15, 3]
B)
[-3, 15]
C)
[-3, 21]
D)
(–, -3] [21, )
For the compound inequality, give the solution set in both interval and graph forms.
170)
-3y+ 5 >-10 or -3y+ 5 2
170)
A)
(–, )
B)
(–, 1] (5, )
C)
(–, 5)
D)
[1, )
Find the indicated intersection or union.
171)
{q, s, u, v, w, x, y, z} {q, s, y, z}
171)
A)
{s, u, w}
B)
{v, x}
C)
{s, u, v, w, x, z}
D)
{q, s, u, v, w, x, y, z}
47
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
172)
11x+ 9 10x+ 1
172)
A)
{x x -8}; ( , -8]
B)
{x x <11}; ( , 11)
C)
{x x -8}; [-8,)
D)
{x x >11}; [11, )
Solve the inequality. Give the solution set in both interval and graph forms.
173)
9x – 1 <-19 and -5 – 6x >1
173)
A)
(–, -2) (-1, )
B)
(-2, -1)
C)
(–, -2)
D)
(–, -1)
Solve by isolating the absolute value and using the absolute value property.
174)
|7k – 9| + 7 =14
174)
A)
2
7, 16
7
B)
2
7
C)
16
7
D)
Solve and check.
175)
1
3y –2=2y + 2 –9y
175)
A)
9
11
B)
9
22
C)
6
11
D)
0
48
Solve and graph. Write the solution in interval notation.
176)
8y – 9 – 4 <-8
176)
A)
–, 5
813
8,
B)
5
8,
C)
D)
5
8, 13
8
Solve the problem.
177)
In order for a chemical reaction to take place, the Fahrenheit temperature of the reagents must be at
139.43°F. Find the Celsius temperature at which the reaction may occur. (F = 9
5C + 32)
177)
A)
282.97°C
B)
59.68°C
C)
–282.97°C
D)
–59.68°C
Solve the equation for the indicated variable.
178)
d = rt; solve for t
178)
A)
t= d –r
B)
t=r
d
C)
t= dr
D)
t=d
r
Write the inequality without “and”.
179)
x –2 and x 2
179)
A)
–2 x 2
B)
2 x –2
C)
–2< x <2
D)
–2 x 2
49
Solve the inequality. Give the solution set in both set–builder notation and graph form.
180)
9x + 6 24 and 5x + 10 25
180)
A)
x x 2 or x 3
B)
x x 2
C)
x x 3
D)
x 2 x 3
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
181)
k
33
181)
A)
{k k 9}; ( , 9]
B)
{k k 9}; [9, )
C)
{k k >9}; (9, )
D)
{k k <9}; ( , 9)
Solve.
182)
A savings bank invests $106,800 in highway bonds and earns 8% per year on the investment. How
much money is earned per year?
182)
A)
$85,440
B)
$8544
C)
$1,335,000
D)
$133,500
Solve the problem.
183)
Jim has gotten scores of 75 and 69 on his first two tests. What score must he get on his third test to
keep an average of 70 or greater?
183)
A)
x 71.3
B)
x >65
C)
x =72
D)
x 66
50
Solve by separating the two absolute values into equal and opposite cases.
184)
4s – 8 =s + 5
184)
A)
–13
3, –3
5
B)
13
3, 3
5
C)
D)
13
3
Find the indicated intersection or union.
185)
{g, r, e, e, n} {b, r, o, w, n}
185)
A)
{g, r, e, e, n, b, r, o, w}
B)
{r, n}
C)
{g, r, e, e, n, b, r, o, w, n}
D)
{g, r, e, e, n, b, o, w}
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
186)
-7 – 2a+ 1 -3a– 10
186)
A)
{a a -4}; ( , -4]
B)
{a a >-2}; (-2, )
C)
{a a -4}; [-4, )
D)
{a a <-2}; ( , -2)
Solve the equation for the indicated variable.
187)
V =1
3Bh; solve for h
187)
A)
h =3V
B
B)
h =V
3B
C)
h =3B
V
D)
h =B
3V
Solve and check. Note that the equation could be an identity or a contradiction.
188)
11 –7(5 – s) +3(s +4) =26
188)
A)
– 19
2
B)
– 15
C)
19
5
D)
31
5
51
For the compound inequality, give the solution set in both interval and graph forms.
189)
–6x + 1 13 or 7x + 3 -25
189)
A)
(–,)
B)
[–4, )
C)
[–4, –2]
D)
[–2, )
Solve using the absolute value property.
190)
9 – x =2
190)
A)
{11}
B)
{7}
C)
{7, –11}
D)
{7, 11}
Solve and graph. Write the solution in interval notation.
191)
2.4 – 3
4w>4.8
191)
A)
–, – 28
536
5,
B)
– 16
5, 48
5
C)
48
5,
D)
–, – 16
548
5,
52
Solve the inequality. Give the solution set in both set–builder notation and graph form.
192)
x –1<3 and x +23
192)
A)
x x < 4
B)
x x 1
C)
x x 1or x > 4
D)
x 1 x < 4
Solve using the absolute value property.
193)
x =6
193)
A)
{-6}
B)
{6}
C)
{6, -6}
D)
{36}
Solve the inequality. Give the solution set in both interval and graph forms.
194)
-37 <5x – 7 and 5x + 7 < –3
194)
A)
(-6, –2)
B)
[-6, –2]
C)
(-6, –2]
D)
[-6, –2)
53
195)
5x – 1 < 4 and x – 2 > –1
195)
A)
(0, 1)
B)
C)
{1}
D)
[0, 1]
Solve.
196)
A report showed that the net profit of a business for one month was $27,753. This was a decrease of
13% from the previous month. What was the previous month’s profit?
196)
A)
$88,532.07
B)
$23,606
C)
$36,047
D)
$31,900
Solve the inequality. Give the solution set in both interval and graph forms.
197)
-23 7x – 2 5
197)
A)
[-3, 1]
B)
[-3, 1)
C)
(-3, 1]
D)
(-3, 1)
54
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
198)
–7<x
5
198)
A)
{x x -35}; [-35, )
B)
{x x >-35}; (-35, )
C)
{x x -35}; ( , -35]
D)
{x x <-35}; ( , -35)
Solve by separating the two absolute values into equal and opposite cases.
199)
4y – 7 =4y + 6
199)
A)
– 1
8, 1
8
B)
1
8
C)
13
8
D)
Find the indicated intersection or union.
200)
{q, s, u, v, w, x}
200)
A)
{q}
B)
{q, s, u, v, w, x}
C)
{q, s, u, v, w}
D)
55
Solve and graph. Write the solution in interval notation.
201)
4–2 – 3x > –4
201)
A)
– 2,
B)
–, – 2
C)
–, – 2 10
3,
D)
– 2, 10
3
202)
6k – 2 – 3 >6
202)
A)
(–, –6) (6, )
B)
11
6,
C)
–, – 7
611
6,
D)
– 7
6, 11
6
Solve.
203)
If nine more than a number is equal to fifteen, what is the number?
203)
A)
-6
B)
15
C)
24
D)
6
56
Solve the equation for the indicated variable.
204)
I =nE
nr + R; solve for n
204)
A)
n = IR(Ir – E)
B)
n =IR
Ir + E
C)
n =-IR
Ir – E
D)
n =-R
Ir – E
Write the inequality without “and”.
205)
x >0 and x <4
205)
A)
0 x 4
B)
4< x <0
C)
0> x >4
D)
0< x <4
Solve the inequality. Give the solution set in both set–builder notation and graph form.
206)
-3x >6 and -3x 18
206)
A)
x -6 x < -2
B)
x 2 < x 6
C)
x 2 x < 6
D)
x -6 < x -2
Solve and graph. Write the solution in interval notation.
207)
5z + 2+412
207)
A)
– 18
5, –2
5
B)
–, –2
5
C)
–2
5, – 18
5
D)
– 8
5, 8
5
57
Solve the problem.
208)
Students in a math class receive a B if the average of their four test scores is between 75 and 85.
Raul scored 71, 82, and 88 on the first three tests. Within what range must his score on the fourth
test lie if he is to get a B?
208)
A)
x 75 x 85
B)
x 59 x 99
C)
x x 59
D)
x 70 x 90
Solve. Write the solution set using set–builder notation and using interval notation. Graph the solution set.
209)
x
2+58
209)
A)
{x x 6}; [6, )
B)
{x x –1}; ( ,–1]
C)
{x x 6}; ( ,6]
D)
{x x <8}; ( ,8)
Use the formula B = P + Prt, which is used to calculate the balance in an account if simple interest is added to a principal P
at an interest rate of r for t years.
210)
Suppose that an account earns 6.3% interest and after five years the balance is $5418.00. Find the
principle that was invested.
210)
A)
$3708.14
B)
$4944.18
C)
$4120.15
D)
$7909.49
Solve the problem.
211)
In order for a chemical reaction to take place, the Fahrenheit temperature of the reagents must be at
least 173.34°F. Find the Celsius temperatures at which the reaction may occur. (F = 9
5C + 32)
211)
A)
C 78.52°
B)
C 344.01°
C)
C 78.52°
D)
C <344.01°
Solve by isolating the absolute value and using the absolute value property.
212)
5x – 4(x + 3) =6
212)
A)
– 9, 3
B)
18
C)
– 18, – 6
D)
6, 18
Solve using the absolute value property.
213)
t + 9 = 0
213)
A)
B)
{-9, 9}
C)
{-9}
D)
{9}
58
Solve and check.
214)
0.4(p +6) –0.9(p +6) =-5
214)
A)
4
B)
0.18
C)
-23.52
D)
-0.48
Solve using the absolute value property.
215)
b – 8 = –6
215)
A)
{14}
B)
{14, 2}
C)
D)
{–14, –2}
Solve by separating the two absolute values into equal and opposite cases.
216)
5s + 3 =s – 9
216)
A)
3, – 1
B)
– 3, 1
C)
D)
– 3
Solve and check.
217)
5(h +4) =20
217)
A)
11
B)
–1
C)
0
D)
16
Solve by isolating the absolute value and using the absolute value property.
218)
2 x +2=17
218)
A)
13
2
B)
15
2
C)
– 15
2, 15
2
D)
– 13
2, 13
2
Find the indicated intersection or union.
219)
{q, s, u, v, w, x, y, z}
{q, s, y, z}
219)
A)
{q, s, y, z}
B)
{q, s, u, v, w, y}
C)
{v, x}
D)
{s, u, v, w, x, z}
Write the inequality without “and”.
220)
x 3 and x <7
220)
A)
7< x 3
B)
3 x >7
C)
3< x 7
D)
3 x <7
Solve the equation.
221)
6x – 8
9=7
221)
A)
B)
-71
6, 71
6
C)
6
-55, 6
71
D)
-55
6, 71
6
Find the indicated intersection or union.
222)
{s, u, g, a, r} {s, a, l, t}
222)
A)
{s, a}
B)
{s, a, l}
C)
{s, u, g, a, r, l, t}
D)
{s}
59
Answer Key
Testname: C2
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Answer Key
Testname: C2
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Answer Key
Testname: C2
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Answer Key
Testname: C2
Answer Key
Testname: C2
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