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Ch. 3 Test Review - Inequalities, Absolute Value, Sets

Total questions: 103

Worksheet time: 26hrs 45mins

Name
Class
Date
1.
Solve the inequality.
x + 5 ≤ 13
a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8 
d)
x ≤ 18 
2.
Match the graph with its inequality.
a)
11 < a
b)
11 > a
c)
 11 ≤ a
d)
 11 ≥ a
3.
Pick the correct letter for:
6 > x
a)
A
b)
B
c)
C
d)
D
4.
-4x + 14 ≤ 54
a)
x ≥ - 10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
5.
Write an expression. 
Anita needs at least an 90 grade (g) on her test to get an A in math class.
a)
g ≤ 90
b)
g ≥ 90
c)
g < 90
d)
g > 90
6.

Solve the inequality.

30 + n ≥ 50

a)

n > 50

b)

n ≥ 80

c)

n < 30

d)

n ≥ 20

7.
Is x = 9 a solution to the given inequality.
x > 9
a)
TRUE
b)
FALSE
8.
Is x = 12 a given solution to the inequality.
x > 5
a)
TRUE
b)
FALSE
9.
What inequality does the number line graph represent. 
a)
x < 2
b)
x > 2
c)
x ≥ 2
d)
x ≤ 2
10.
Will my dot be colored in?
5 ≥ x
a)
Yes
b)
No
11.
Pick the correct inequality.
a)
A
b)
B
c)
C
d)
D
12.
2x+6>12
a)
x>9
b)
x>3
c)
x<9
d)
x<3
13.
-3 + x ≤ -11
a)
x ≤ -8
b)
x ≤ 8
c)
x ≥ -8
d)
x ≥ 8
14.
.5(x - 8) < 2 
a)
x > 20
b)
x < 20
c)
x > 12
d)
x < 12
15.
-1(2x + 4) ≥ 6
a)
x ≤ -5
b)
x ≥ -5
c)
x ≤ -1
d)
x ≥ -1
16.
What inequality is graphed here?
a)
x > 1
b)
x ≥ 1
c)
x < 1
d)
x ≤ 1
17.
What inequality is graphed here?
a)
x ≤ -2
b)
x < -2
c)
x > -2
d)
x ≥ -2
18.

Translate: 5 times a number is at least 60.

a)

5x < 60

b)

5x > 60

c)

5x ≤ 60

d)

5x ≥ 60

19.

Translate:

A number increased by 4 is no more than -18.

a)

x + 4 < -18

b)

x + 4 > -18

c)

x + 4 ≤ -18

d)

x + 4 ≥ -18

20.

Translate:

Twice a number is smaller than 42.

a)

2x < 42

b)

2x > 42

c)

2x ≤ 42

d)

2x ≥ 42

21.
more than
a)
<
b)
>
c)
≤
d)
≥
22.
At Least
a)
<
b)
>
c)
≤
d)
≥
23.
No More Than
a)
<
b)
>
c)
≤
d)
≥
24.
less than or equal to
a)
<
b)
>
c)
≤
d)
≥
25.
Less Than
a)
<
b)
>
c)
≤
d)
≥
26.
- 2k > 18
a)
k is greater than 20
b)
k is less than negative 9
c)
k is greater than negative 9
d)
k is less than 36 
27.
8x ≥ -32
a)
x ≥ -4
b)
x ≥ 4
c)
x ≤ -4
d)
x ≥ 4
28.
7b - 3 < 11
a)
b < 2
b)
84 > b
c)
b > 2
d)
b < 84
29.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥ 
c)
≤, <
d)
≥, >
30.
When you graph an inequality, you used a closed dot when you use which symbols?
a)
≤, ≥ 
b)
<, >
c)
≤, <
d)
≥, >
31.

Which graph matches the inequality

k < 3?

a)

A

b)

B

c)

C

d)

D

32.
Which graph matches the inequality
2 > p?
a)
A
b)
B
c)
C
d)
D
33.
Write an inequality for Graph 3.
a)
x ≤ -2 AND x > 5
b)
x ≤ -2 OR x > 5
c)
x ≥ -2 OR x < 5
d)
-2 ≤ x < 5
34.
0 < x + 7 < 9
a)
-7<x   and   x<2
b)
-7<x   or   x<2
c)
-7>x   and   x>2
d)
-7>x  or   x>2
35.
x+2<-4 or -5x<-15
a)
-6<x<3
b)
x<-3 and x>6
c)
x<-6 or x>3
d)
No Solution
36.
2<x+2<5
a)
0<x<3
b)
4<x<7
c)
4<x<3
d)
0<x<7
37.
Write an inequality for Graph 4.
a)
-2 < x < 5
b)
x < -2 or x > 5
c)
x ≥ -2 OR x < 5
d)
-2 ≤ x ≤ 5
38.
What inequality is graphed? 
a)
x > 2 and x ≤ -3
b)
x > 2 and x < -3
c)
x > 2 or x ≤ -3
d)
x > 2 or x < -3
39.

What inequality is graphed?

a)

x > 2 and x < 4

b)

2 ≤ x ≤ 4

c)

x > 2 or x < 4

d)

x ≥ 2 or x ≤ 4

40.

Which of the following would result in NO SOLUTION?

a)

x < 1 or x > 5

b)

x > 1 or x < 5

c)

x < 1 and x > 5

d)

x > 1 and x < 5

41.
Solve and graph:
a)
A
b)
B
c)
C
d)
D
42.
Write an inequality for Graph 3.
a)
x ≤ -2 AND x > 5
b)
x ≤ -2 OR x > 5
c)
x ≥ -2 OR x < 5
d)
-2 ≤ x < 5
43.
Solve for x
l 5x l = 40
a)
x = 8 and x =-8
b)
x = 35 and x = -35
c)
Only x = 8
d)
No Solution
44.
Solve for x
l 2x−1 l = 9
a)
x = 5 and x =-4
b)
x = 5 and x = -5
c)
Only x = 5
d)
No Solution
45.
Solve for x
l 4x−3 l = 17
a)
x = 5 and x =-3.5
b)
x = 0 and x = -5
c)
x = 10 and x = -10
d)
No Solution
46.
Solve for x
l 3x + 2 l = 5
a)
x = -2.333... and x = 1
b)
x = 4 and x = 8
c)
x = 0
d)
No Solution
47.
Solve for x
l 2x−1 l +4 = 8 
a)
x = 2.5 and x = -1.5
b)
x = 2 and x = -1
c)
x = -2 and x = 9
d)
No Solution
48.
Solve for x
l x−6 l + 4= 10
a)
x = 12 and x = 0
b)
x = 3 and x = -3
c)
x = -12 and x = 0
d)
No Solution
49.
Solve for x
3 l 4w−1 l −5 = 10
a)
x = 1.5 and x =-1
b)
x = -1.5 and x = 1
c)
x =1 and x = -1
d)
No Solution
50.
Solve for x
2 lx−4l+8=18
a)
x = 9 and x =-1
b)
x = 1 and x = -9
c)
x= 4 and x = -2
d)
No Solution
51.
|v + 8| − 5 = 2 
a)
{-1,-15}
b)
{-1,-5}
c)
{-15,15}
d)
No Solution
52.
Solve:
 |x + 3| > 8
a)
x > 5 or x < -11
b)
x > 5
c)
all real numbers
d)
no solution
53.
Solve:
|x + 3| > - 8
a)
x > 5 or x < -11
b)
x > 5
c)
all real numbers
d)
no solution
54.
Solve:
3 | 2x + 7| - 7 < -4
a)
x < -3 and x > -5/3
b)
x < -3 and x > -4
c)
all real numbers
d)
no solution
55.
Solve:
3 | 2x + 7| + 7 < 4
a)
x < -3 and x > -5/3
b)
x < -3 and x > -4
c)
all real numbers
d)
no solution
56.
Solve:
|x + 4| + 8 > 2
a)
x < -3 and x > -5/3
b)
x < -3 and x > -4
c)
all real numbers
d)
no solution
57.
Solve:
|x + 4| - 8 > 2
a)
x > 6 and x < 10
b)
x > 6 or x < -14
c)
all real numbers
d)
no solution
58.
Solve.
|2x - 1| = -7
a)
x = -3 or x = 4
b)
all real numbers
c)
x = 3 or x = -3
d)
no solution
59.
Solve.
-5|x - 4| > -20
a)
x < 8 and x > 0
b)
x > 8 or x < 0
c)
all real numbers
d)
no solution
60.
Solve.
-5|x - 4| > 20
a)
x < 8 and x > 0
b)
x > 8 or x < 0
c)
all real numbers
d)
no solution
61.
a)
v>5 or v<-5
b)
v≥5 or v≤-5
c)
v>-5 or v<5
d)
all real numbers
62.
a)
r > 11/4 or r < 9/4
b)
r > 5 or r ≤ 0
c)
r > 5 or r < 0
d)
r < -5 or r > 0
63.
What type of set is denoted as either { } or ∅?
a)
Universal Set
b)
Empty (or Null) Set
c)
Disjointed Set
d)
Complement of a Set
64.

What does this symbol ( ∪ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

65.
What does this symbol ( ∩ ) represent in set theory?
a)
Union
b)
Intersection
c)
Disjointed
d)
Subset
66.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

67.
The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?
a)
{-4, -3, -2, -1, 0, 1, 2, 3}
b)
{-3, -2, -1, 1, 2, 3}
c)
{-4, -3, -2, -1, 1, 2, 3, 4}
d)
{-4, -3, -2, -1, 1, 2, 3}
68.
What statement does the shaded region represent?
a)
A ∩ B ∩ C
b)
A  ∪ B ∩ C
c)
B ∩ C
d)
A ∪ C
69.
X ∩ Y ∩ Z
a)
{ }
b)
{Phillip}
c)
{Billy, Phillip, Bryan, Perez}
d)
{Billy, Perez, Bryan}
70.
How many students do not ski or ice skate?
a)
10
b)
16
c)
22
d)
28
71.
From the above Venn diagram, what is the set S ∩ T?
a)
{casey, drew, jade, glen}
b)
{alex, casey, drew,hunter}
c)
{casey, drew}
d)
{drew, jade}
72.
A = {1, 3, 5, 7, 9}
B = {2, 3, 5, 7}
What is A ∩ B ?
a)
{3, 5, 7}
b)
{2, 3, 5, 7}
c)
{2, 3, 5, 7, 9}
d)
{1, 2, 3, 5, 7, 9}
73.

Write the following solution in set builder notation:


x ≥ -2

a)

{ x | x ≥ 2 }

b)

{ x | x ≥ -2 }

c)

{ x ≥ -2 }

d)

{ x | x ≤ -2 }

74.

Write the following solution in set builder notation:

y > 10

a)

{ y > 10 }

b)

{ y | y > 10 }

c)

{ y | y < 10 }

d)

( -0, 10 )

75.

When writing a solution in interval notation, what brackets do i use for:

> or <

a)

[ ]

b)

( )

76.

When writing in interval notation, what kind of brackets do I use for:

or ≤ or ≥

a)

[ ]

b)

( )

77.

Write the following solution in interval notation:

x ≥ -3

a)

[ -3, ∞ )

b)

( -3, ∞ )

c)

( -∞ , -3 )

d)

( -∞ , -3]

78.

Write the following solution in interval notation:

z < 20

a)

( -∞ , 20 )

b)

( 20,∞)

c)

( -∞ , 20)

d)

( -∞ , 20]

79.

Write the following solution in interval notation:

x ≥ 6

a)

( -∾ , 6]

b)

( -∾ , 6 )

c)

( 6, ∾ )

d)

[ 6, ∾ )

80.

When graphing an inequality solution, what type of circle do I draw for the symbol:

> or <

a)

open circle

b)

closed circle

81.

When graphing an inequality solution, what type of circle do I draw for the symbol:

or ≤ or ≥

a)

Closed Circle

b)

Open Cirlce

82.

Why do I draw a closed circle when it's less than or equal to or greater than or equal to?

a)

Because we are INCLUDING that solution

b)

Because we are NOT INCLUDING that solution

83.

Given:

x ≤ -10

Is -25 a solution?

a)

Yes, it is a solution.

b)

No, it is not a solution.

84.

Given:

x > 15

Is -25 a solution?

a)

Yes, it is a solution.

b)

No, it is not a solution.

85.

Identify B'

a)

{4}

b)

{8}

c)

{1, 2, 3, 8, 10]

d)

{1, 2, 3, 10}

86.

Which of the following are the elements of the A={x/x is a whole number}

a)

{2, 4, 6}

b)

{0, 1, 2, 3, 4,......}

c)

{1, 2, 3, 4, 5,...}

87.

What is the set builder notation for B = {9, 18, 27, 36, 45, 54,...}

a)

B = {x/x is a multiple of 9}

b)

B = {x/x is a power of 9}

88.

What symbol will make the statement,    { } ____{1, 18, 20, 21} , true?

a)

 ⊆\subseteq  

b)

 ⊈\not\subseteq  

c)

 ∪\cup  

d)

 ==  

89.

Given that X = { 5, 6, 7, 8, 9, 10} and Y = {x/x is an even number less than 10}. What is the result when you operate X∪YX\cup Y ? 


a)

{6, 8}

b)

{2, 4, 6, 8, 10}

c)

{2, 4, 5, 6, 7, 8, 9, 10}

d)

{0, 2, 4, 5, 6, 7, 8, 9, 10}

90.

Consider the sets P = { x/x is a distinct letter in the word school} and Q = {x/x is a consonant in the word book}. What are the elements of P∩QP\cap Q ? 


a)

{o}

b)

{ }

c)

{b, c, h, k, l, o, s}

91.

Given that U ={ x/x is an integer} and L = {x/x is a negative integer}. What is L'?

a)

{0, 1, 2, 3, 4, 5, 6,....}

b)

{1, 2, 3, 4, 5,....}

c)

{ 0 1/2, 1, 1 1/2, 2, 2 1/2,....}

92.
Express the following in Interval Notation
-8 ≤ x < 8
a)
[-8, 8]
b)
[-8,8)
c)
(-8, 8]
d)
(-8, 8)
93.
Express the following in Interval Notation
-9 < x ≤ -4
a)
[-9, -4]
b)
(-9,-4]
c)
[-9, -4]
d)
(-9,-4)
94.
Express the following interval in Set notation:
(-7, 15]
a)
-7 ≤ x ≤ 15
b)
-7 < x ≤ 15
c)
-7 ≤ x < 15
d)
-7 < x < 15
95.
Express the following interval in Set notation:
[3, 5]
a)
3 ≤ x ≤ 5
b)
3 < x ≤ 5
c)
3 ≤ x < 5
d)
3 < x < 5
96.
Look at the graph. Write the inequality in interval notation.
a)
(-2,5)
b)
(-∞,-2)⋃(5,∞)
c)
[-2,5]
d)
(-∞,-2]∪[5,∞)
97.
Write the following in interval notation
x < 3 or x ≥ 5
a)
(3, -∞) or (∞, 5]
b)
[-∞, 3) or [5, ∞]
c)
(-∞, 3) or [5, ∞)
d)
(3, -∞] or [∞, 5]
98.
Look at the picture. Which number line corresponds to [-2, 5]?
a)
Graph 1
b)
Graph 2
c)
Graph 3
d)
Graph 4
99.

Write the following solution in set builder notation:


x ≥ -2

a)

{ x | x ≥ 2 }

b)

{ x | x ≥ -2 }

c)

{ x ≥ -2 }

d)

{ x | x ≤ -2 }

100.
Write the set of numbers inset-builder notation.
(−∞, 5] or [14, ∞)
a)
{x∣x ≤ 5 or x > 14}
b)
{x∣x ≤ 5 or x ≥ 14}
c)
{x∣x < 5 or x > 14}
d)
{x∣x ≤ 5 or x > 14}
101.
Write the set of numbers inset-builder notation.
(22, 98]
a)
{x ∣ 22 < x ≤ 98 }
b)
{x ∣ 22 ≤ x ≤ 98 }
c)
{x ∣ 22 ≤ x < 98 }
d)
{x ∣ 22 < x < 98 }
102.
Express the following in Interval Notation
{ x  | -8 ≤ x < 8 }
a)
[-8, 8]
b)
[-8,8)
c)
(-8, 8]
d)
(-8, 8)
103.
What set notation does the number line graph represent?
a)
{x| x ≥-5 }
b)
{x| -5 ≥ x }
c)
{x| -5 ≥∞}
d)
{x| -5 ≤ x < ∞ }

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