Homework
Answers
Standardized Test Prep & Mixed Review P. 192 #s 58-68
all

58)
62)
59)
63)
60)
64)
61)
65)
Homework Answers
Standardized Test Prep & Mixed Review P. 192 #s 58-68
all

66) Whole numbers
67) Natural numbers
68) Integers
Homework
Answers
Standardized Test Prep & Mixed Review P. 199 #s 53-66
all

Homework
Answers
Standardized Test Prep & Mixed Review P. 199 #s 53-66
all

Section
3
–
5

Working With Sets
Objectives:
To write sets and identify subsets
To find the complement of a set
Warm-Up

Set:
 A collection of distinct elements

Subset:
 Contains elements from a set
Writing Sets

Roster Form
 Lists the elements of a set within braces { }
Example:
Set-Builder Notation
 Describes the properties of the elements in the set
Example:
Problem # 1
Using Roster Form &
Set-Builder Notation

How do you write “T is the set of natural numbers that are
less than 6” in roster form? In set-builder notation?
Problem # 1
Got it?

N is the set of even natural numbers that are less than
or equal to 12.
How do you write N in roster form?
How do you write N in set-builder notation?
Problem # 2
Inequalities and Set-Builder Notation

a)
How do you write the solutions of -5x+7 ≤ 17 in
set-builder notation?
Problem # 2
Inequalities and Set-Builder Notation

b)
How do you write the solutions of 9 – 4n > 21 in
set-builder notation?
Problem # 2
Got it?

In set-builder notation, how do you write the solutions
of -4x + 3 < 15?
You know that a set A is a subset of a set
B if each element of A is also an element
of B.

Example:
If B = {-2, -1, 0, 1, 2, 3} and A = {-1, 0, 2},
then A is a subset of B.
Written as A ⊆ B
Empty Set:

The set that contains no elements.
**The empty set is a subset of every set.
*Use ∅ or { }
Problem # 3
Finding Subsets

a)
What are the subsets of the set {3, 4, 5}?
Problem # 3
Finding Subsets

b)
What are the subsets of the set {1, 2}?
Problem # 3
Finding Subsets

c)
Let A = 𝒙 𝒙 < −𝟑 and B = 𝑥 𝑥 ≤ 0 . Is A a
subset of B? Explain.
Problem # 3
Got It?

What are the subsets of the set P = {a, b, c}?
Classwork & Homework
Assignment

 3 – 5 Worksheet #s 1-23 all
Homework Answers
3-5 Practice Form G #s 1-23 all
1) M = {-4, -3, -2, -1, 0, . . .} M = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟, 𝑥 > −5
2) N = {2, 0, -2, -4, -6. . .} N = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 < 2.5
3) P ={1, 5, 25}
P = 𝑥 𝑥 𝑖𝑠 𝑎 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 25
4) R = 1, 3, 5, 7, 9, 11
R = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑜𝑑𝑑 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 < 12
5) B = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟, 𝑥 ≥ −3
6) M = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 < 11
7) S = 𝑥 𝑥 𝑖𝑠 𝑎 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 18
8) G = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑜𝑑𝑑 𝑖𝑛𝑡𝑒𝑔𝑒𝑟
9) 𝑦 𝑦 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑦 < 8
10) 𝑟 𝑟 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑟 > 20
11) 𝑚 𝑚 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑚 ≤ −6

Homework Answers
3-5 Practice Form G #s 1-23 all
12) 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 ≥ 8/3
13) 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 ≻ −6
14) 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 ≥ 0
15) 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 < 1/3
16) 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 > 3
17) 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 ≥ −8
18) { }, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c},
{a,b,d} , {a,c,d} , {b,c,d} {a, b, c, d}
19) { }, {0}, {3}, {6}, {9}, {0, 3}, {0, 6}, {0, 9}, {3, 6}, {3, 9}, {6, 9}, {0, 3, 6},
{0, 3, 9}, {0, 6, 9}, {3, 6, 9}, {0, 3, 6, 9}
20) { }, {car}, {bus}, {truck}, {car, bus}, {car, truck}, {bus, truck}, {car,
bus, truck}
21) { }, {-5}, {5}, {-5, 5}
22) { }, {0}
23) { }, {red}, {blue}, {yellow}, {red, blue}, {red, yellow}, {blue,
yellow}, {red, blue, yellow}

Homework Answers
3-5 Reteaching #s 1-13 all

Homework Answers
3-5 Reteaching #s 1-13 all

Homework Answers
3-5 Practice Form K #s 1-23 all
1) M = {-4, -3, -2, -1, 0, . . .} M = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟, 𝑥 > −5
2) N = {2, 0, -2, -4, -6. . .} N = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 < 2.5
3) P ={1, 5, 25}
P = 𝑥 𝑥 𝑖𝑠 𝑎 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 25
4) R = = 𝑥 𝑥 𝑖𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 0 𝑎𝑛𝑑 12
1) 𝑦 𝑦 < 8
6) 𝑟 𝑟 > 210
7) 𝑚 𝑚 ≤ −6
8) 𝑥 𝑥 ≥ 8/3
9) 𝑥 𝑥 > −6
10) 𝑥 𝑥 ≥ 0
11) { }, {x}, {y}, {z}, {x,y}, {x,z}, {y,z}, {x,y,z}
12) { }, {0}
13) { }, {car}, {boat}, {airplane}, {car, boat}, {car, airplane}, {boat,
airplane}, {car, boat, airplane}
14) { }, {-2}, {2}, {-2, 2}
15) A’={0, 5, 9}
16) R’ ={-4, -2, 0}
17) yes, each element of A is in U 18) no, 11 is not in B
19) no, 15 is not in A
20) A’ = {Mon., Tues., Wed., Thurs., Fri.}
A’ = 𝑥 𝑥 𝑖𝑠 𝑎 𝑤𝑒𝑒𝑘 𝑑𝑎𝑦

3 – 5 Working

With Sets
Continued
Objectives:
To write sets and identify subsets
To find the complement of a set
Warm-Up

Universal Set:
 The largest set you are using.

Complement of a Set:
 The set of all elements in the universal set that are
not in the set.
*The complement of A is A’
Problem # 4
Finding the Complement of a
Set

a)
Universal Set U = {months of the year} and set A =
{months with exactly 31 days}. What is the complement
of set A? Write your answers in roster form.
Problem # 4
Finding the Complement of a
Set

b)
Given that the universal set U = {car, truck, van,
school bus, bicycle} and the set A is the set of all vehicles
that have 4 wheels, what is the complement of set A?
Problem # 4
Finding the Complement of a
Set

c)
Universal Set U = {1, 2, 3, 4, 5} and set A = {2, 3}.
What is A’?
Problem # 4
Got It?

Universal Set U = {…-3, -2, -1, 0, 1, 2, 3, …} and set A =
{…-3, -1, 1, 3, …}. What is A’?
Classwork Assignment

 3–5 Practice Form G #s 24-32 all
Homework Assignment

 3–5 Practice Form G #s 24-32 all
Homework Answers
3-5 Practice Form G #s 24-32 all

24)
25)
31)
26)
27)
28)
32)
29)
30)
3
–6
Objectives:
To write sets and identify subsets
To find the complement of a set
Warm-Up

Interval Notation:

 Used to describe an interval on the number line,
using three special symbols:
 Parenthesis:
 Brackets:
 Infinity:
Problem # 5
Using Interval Notation

a) What is the graph of [-4, 6)? How do you write [-4, 6)
as an inequality?
b) What is the graph of (-∞, 2]? How do you write (-∞, 2] as
an inequality?
Problem # 5
Using Interval Notation

c) What is the graph of x ≤ -1 or x > 2? How do you
x ≤ -1 or x > 2 in interval notation?
write
d) What is the graph of x < -2 or x ≥ 1? How do you write x
< -2 or x ≥ 1 in interval notation?
Problem # 5
Got It?

a) What is the graph of (-2, 7]? How do you write (-2, 7] as
an inequality?
b) What is the graph of y > 7? How do you write y > 7 in
interval notation?
Classwork Assignment

3-6 Pp. 204 – 205 #s 23-34 all
Homework Assignment

3-6 Pp. 204 – 205 #s 23-34 all
Homework Answers
23)
3-6 Pp. 204 – 205 #s 23-34 all

24)
25)
26)
Homework Answers

27)
28)
29)
Homework Answers

30)
31)
32)
Homework Answers
33)

34)
3–6

Compound
Inequalities
Objectives:
To solve and graph inequalities containing the word and
To solve and graph inequalities containing the word or
Warm-Up

Inequality ______________________
Classwork Assignment

3-6 Practice Form G #s 13-22 all
Homework Assignment

3-6 Practice Form G #s 13-22 all
Classwork Assigment
