Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve and graph the solution set on a number line.
1)
|5x – 9| – 4 >1
1)
A)
4
5, 14
5
B)
C)
14
5, 4
5
D)
–, 4
514
5,
Graph the inequality.
2)
x
3+y
2 1
2)
1
A)
B)
C)
D)
Graph the inequality in a rectangular coordinate system.
3)
2x + y –3
3)
2
A)
B)
C)
D)
3
Solve the compound inequality. Other than , graph the solution set on a number line.
4)
8x – 10 < – 10 and 9x – 4 –40
4)
A)
(–4, 0]
B)
[–4, 0]
C)
[–4, 0)
D)
(–4, 0)
Solve.
5)
An office manager is buying used filing cabinets. Each small file cabinet costs $7, takes up 6 square
feet of floor space, and holds 9 cubic feet of files. Each large file cabinet costs $11, takes up 8 square
feet of floor space, and holds 13 cubic feet of files. The total cost cannot exceed $136, and the office
has no more than 108 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?
5)
A)
0 small file cabinets and 16 large file cabinets; 208 cubic feet
B)
16 small file cabinets and 0 large file cabinets; 144 cubic feet
C)
6 small file cabinets and 10 large file cabinets; 220 cubic feet
D)
10 small file cabinets and 6 large file cabinets; 168 cubic feet
Solve and graph the solution set on a number line.
6)
2(x + 1) +46
6)
A)
(–6, 0)
B)
(–4, 2)
C)
[–4, 2]
D)
[–6, 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.
7)
x >4 or x <4
7)
A)
(–, 4)
B)
C)
(4, )
D)
(–, 4) (4, )
Solve.
8)
Every Sunday, Jarod buys a loaf of fresh bread for his family from the corner bakery for $4.00. The
local department store has a sale on breadmakers for $97. If the bread–making supplies cost $0.93
per week, for how many weeks would Jarod have to bake a loaf of bread at home before the
breadmaker starts saving him money?
8)
A)
At least 31 weeks
B)
At least 32 weeks
C)
At least 34 weeks
D)
At least 33 weeks
Graph the inequality.
9)
y x – 5
9)
A)
B)
C)
D)
6
Find the value of the objective function at each corner of the graphed region. Use this information to answer the question.
10)
Objective Function z =8x + 9y
What is the minimum value of the objective function?
10)
A)
0
B)
117
C)
50
D)
51
Graph the inequality.
11)
y >4x + 3
11)
A)
B)
7
C)
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
12)
y 4x – 4
y > – 2
3x
12)
A)
B)
8
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.
13)
–35x
3– 8 <7
13)
A)
(3, 9]
B)
[3, 9)
C)
[3, 4)
D)
(3, 4]
Solve.
14)
A bakery plans to market a mixed assortment of its two most popular cookies, Chocolate Chip and
Toffee Chunk. The marketing analyst proposes that the new assortment be constrained by the
inequality 3C + 4T
31, where C is the number of Chocolate Chip cookies and T is the number of
Toffee Chunk cookies. The sales analyst suggests that the assortment should be constrained by the
inequality 5C + 2T
33. The number of each type of cookie cannot be negative, so C 0 and T 0.
Graph the region satisfying all the requirements for the assortment using C as the horizontal axis
and T as the vertical axis. Does the combination of 6 Chocolate Chip cookies and 3 Toffee Chunk
cookies satisfy all of the requirements?
14)
9
A)
Yes
B)
No
C)
Yes
D)
No
Graph the inequality.
10
15)
y >6
15)
A)
B)
C)
D)
Find the union of the sets.
16)
{f, g, h, k, m}
16)
A)
{h, m}
B)
{f, g, h, k, m}
C)
{f}
D)
Solve and graph the solution set on a number line.
17)
3(5x + 6) <18x + 9
17)
A)
( , 3)
B)
[3, )
C)
(3, )
D)
( , 3]
C
12
B
Solve the inequality. Other than , graph the solution set on a number line.
18)
42x – 42 >6(6x – 2)
18)
A)
( , 5]
B)
(5, )
C)
( , 5)
D)
[5, )
Graph the inequality.
19)
y < x + 6
19)
A)
B)
13
C)
D)
Solve the inequality. Other than , graph the solution set on a number line.
20)
–6x + 6 + 9x <6+ 1x + 10
20)
A)
(5, )
B)
[5, )
C)
( , 5]
D)
( , 5)
14
21)
–2x 18
21)
A)
[–9, )
B)
( , 9]
C)
( , –9]
D)
[9, )
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.
22)
33x – 3 15
22)
A)
(2, 6)
B)
[2, 6]
C)
(–, 2) (6, )
D)
(–, 2] [6, )
B
Find the intersection of the sets.
23)
{–3, 0, 2, 4}
{2, 4, 9}
23)
A)
{2, 4}
B)
{–3, 0, 2, 4}
C)
{2, 4, 9}
D)
{–3, 0, 2, 4, 9}
A
C
Solve.
24)
When a number is subtracted from –7, the absolute value of the difference is more than 3. Use
interval notation to express the set of all numbers that satisfy this condition.
24)
A)
( , –10) (–4, )
B)
( , –10] [–4, )
C)
(–10, –4)
D)
( , –4) (10, )
Graph the inequality.
25)
y x – 4
25)
A)
B)
C)
D)
A
Solve the problem.
26)
A doctor has told a sick patient to take vitamin pills. The patient needs at least 53 units of vitamin
A, at least 11 units of vitamin B, and at least 47 units of vitamin C. The red vitamin pills cost 10¢
each and contain 8 units of A, 1 unit of B, and 2 units of C. The blue vitamin pills cost 20¢ each and
contain 3 units of A, 1 unit of B, and 7 units of C. How many pills should the patient take each day
to minimize costs?
26)
A)
6 red and 5 blue
B)
7 red and 4 blue
C)
5 red and 6 blue
D)
11 red and 0 blue
Write a system of three inequalities that describes the given constraints.
27)
Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 8 hours to
make a hat and 3 hours to make an afghan, and she has no more than 58 hours available. She has
material for no more than 11 items, and she wants to make at least two afghans. Let x = the number
of hats she makes and y = the number of afghans she makes.
27)
A)
8x +3y 58, x + y 11, y 2
B)
3x +8y 58, x + y 11, x
2
C)
8x +3y 58, x + y 11, x
2
D)
8x +3y 58, x + y 11, y 2
Solve the linear inequality. Other than , graph the solution set on a number line.
28)
5(4x +7) – 4x < 4(8+ 4x) – 6
28)
A)
( , 7)
B)
(7, )
C)
D)
( , )
Graph the solution set of the system of inequalities or indicate that the system has no solution.
17
29)
–1
y <10
29)
A)
B)
C)
D)
18
Solve and graph the solution set on a number line.
30)
x
7–1
4x
4+1
30)
A)
–, –35
3
B)
, –35
3
C)
–35
3,
D)
–35
3,
Find the solution set for the equation.
31)
|–3x – 6| = |–2x – 8|
31)
A)
2
B)
C)
2, 14
5
D)
2, –14
5
D
32)
|x – 8| = |9 – x|
32)
A)
17
2
B)
1
2
C)
D)
{17}
A
C
Find the union of the sets.
33)
{–3, 0, 1, 4} {1, 4, 8}
33)
A)
{1, 4}
B)
{–3, 0, 1, 4}
C)
{1, 4, 8}
D)
{–3, 0, 1, 4, 8}
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)
–4x > – 12 and x +4>3
34)
A)
(–1, 3)
B)
C)
(3, )
D)
(–, –1) (3, )
A
Solve the inequality. Other than , graph the solution set on a number line.
35)
x
33+x
12
35)
A)
(12, )
B)
[–12, )
C)
(–, 12]
D)
[12, )
D
D