Algebra Textbook Volume 1 Student Edition wc

Practice 4.4 B Name _______________________

Complete the following table: Graphs

Words Algebraic Expressions 13

1) Numbers greater 58
than 1 and less than 03
3 02
5 10
2) −3 0
5<x<8 34
−5 −2
3) Numbers less than 0≤x<2 68
or equal to 0 or 10 12
greater than 3

4)

5)

6) Numbers less than
−3 or greater than 0

7)

8)
x < −5 or x > −2

9)

10) Numbers between
10 and 12

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Practice 4.4 C Name _______________________

Complete the following table: Graphs

Words Algebraic Expressions −1 3
36
1) −4 4
−10 −5
2) x < 3 or x > 6 −6 −1

3) Numbers between −7 −5
−4 and 4, inclusive 05
59
4) −7 −2

5) Numbers less than −2 8
−6 or greater than
−1

6)

7) Numbers less than
0 or greater than 5

8)

9) Numbers greater
than −7 and less
than −2

10)

2<x≤8

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Practice 4.4 D Name _______________________

Complete the following table:

Words Algebraic Expressions Graphs

1) −9
−9
2) −9 < x ≤ −7 5 −5
x < −9 or x > −6 −8 −7
3) Numbers less than 5 or 7
greater than or equal to 4 −6
7 −9
1 12
4) Numbers between −8 −2 −6
and −6 −10 3
1 1
5) Numbers greater than 0
4 and less than 12 8

6)

7) Numbers between 1
and 3, inclusive

8)

9) Numbers less than −10
or greater than 0

10)

x < 1 or x > 8

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4.5 Solving Compound Inequalities Name _______________________________

Solving a compound inequality means isolating the variable in the expression−
getting the variable all by itself.

Compound Inequalities with “and”

This procedure requires two steps and these steps must be applied to all three parts
of the expression. The goal is to get the variable by itself in the center
( ______ < x < _________ ).

Step 1
Use addition or subtraction to get rid of the constant in the center portion.
Ex: 19 < 2x+5 < 29

−5 −5 −5
14 < 2x < 24
Note: The five is subtracted in three places!
Step 2
Multiply or divide to get the coefficient of the variable in the center equal to one.
14 2 24
Ex: 2 < 2 < 2
7 < x < 12
Note: Division by 2 is done in three places!

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4.5 A cont’d Name ______________________

Note: In this procedure, the inequality symbols are simply copied over.

Examples:

1) 15 ≤ 3x+6 < 33

2) −15 < 4x−7 < −7

3) −22 ≤ 5x+8 ≤ 58

4) 7 ≤ 2x−3 < 27
5) −1 < 21x+5 ≤ 15

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4.5 A cont’d Name ________________________

Compound Inequalities with “or”

The procedure here involves solving the two inequalities separately and then stating
the two solutions joined by the word “or.”

Ex:

4x−8 < 16 or 3x+5 ≥ 32
−5 −5
+8 +8

4 24 3 27
4 < 4 or 3 ≥ 3

x < 6 or x ≥ 9

Examples:
1) 6x+5 < −7 or 3x+8 > 8

2) 4x−8 < 4 or 7x+7 > 70

3) 3x+9 < −6 or 8x−4 > −20

4) 12x−11 < 1 or 9x+8 > 53

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Practice 4.5 B Name __________________________

Solve these compound inequalities and then graph the solutions.
1) −11 ≤ 2x−5 ≤ 13

2) 5x−6 < 4 or 3x+7 > 16

3) 25 ≤ 3x+4 < 37

4) 3x+10 < −8 or 2x−7 > −11
5) −52 < 5x−12 < −22

6) 4x−9 < −9 or 7x+11 ≥ 46
7) 4 < 21x + 6 < 13
8) 6x+7 < 37 or 8x−14 > 50
9) −15 ≤ 6x−9 < 3

10) 9x−6 ≤ −60 or 4x+9 ≥ −3

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Practice 4.5 C Name __________________________

Solve these compound inequalities and then graph the solution:

1) 29 < 9x+20 < 110

2) 3x−5 < −20 or 6x+10 > 4

3) −1 < 2x −9 ≤ 11

4) 4x+7 < 15 or 8x−16 > 40

5) −1 ≤ 3x+11 ≤ 20
6) 2x−7 ≤ −13 or 5x+8 ≥ 18

1
7) −4 < 2x−8 < −1

8) 6x−18 < 12 or 3x+6 > 33

9) −17 ≤ 4x+11 ≤ −5

10) 4x +17 ≤ 13 or 3x−20 ≥ −2

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Chapter 4 Cloze

Chapter 4 introduces inequalities, one−step through multi-step and compound
inequalities. This chapter builds on the material presented in Chapter Two-- the solving
of equations:

Chapter 2: 3x = 10 + x vs Chapter 4: 3x < 10 + x.

The method of solving equations and the method for solving ___inequalities____
mirror each other; they both utilize the __four___-step method, in the same order:

Step one - distribute
Step two - combine __like___terms on the two sides of the inequality sign (<
or >), separately
Step three - add or __subtract__ to get the terms with x on one side of the
equals sign and the terms without x on the other

Note: It is recommended that the solution of these equations
keeps x on the left of the equals sign. This will lead to less
confusion in more advanced problems!
Step four: multiply or ____divide____ to get the coefficient of x equal to one.

4.1

Explanation of Inequalities: Algebraic Expressions and Graphing

Inequalities are similar to equations but, in place of the equals sign, one of the

following is used:

Symbol Definition

_______>__________________ ____greater than____________

_______<__________________ _____less than________________

_______ > ______________ _greater than or equal to__

_______ < ______________ ____less than or equal to____

Inequality Words
x > −3 x is greater than −3
x≤5
x is less than or equal to 5
x<8
x ≥ 15 x is less than 8

x is greater than or equal to 15

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4.1 (cont.)
Students:

x < −5 x is less than −5
x≥9 x is greater than or equal to 9
x>3 x is greater than 3
x≤7 x is less than or equal to 7

4.1 cont’d
In the graphs for these inequalities, a __closed___ circle is used with the symbols
____ > (underlined) and < (underlined) to indicate that the
__endpoint____ (the point at the end) __is___ included. In the graphs for these
inequalities, an __open___ circle is used with the symbols > and < to indicate that
the ____endpoint____ ____is____ ____not___ included.

4 < x < 8 is read
____4 is less than x which is less than 8 ____. It refers to the numbers
between ___4_______ and ____8_______, not including the __endpoint___. The graph
would be:

048
4.2 A
Solving Simple One-Step Inequalities
Simple one-step inequalities are solved the same way as simple equations. The object
is to get ___x_____ alone on the ____left___. To do that, we have to get rid of the
number on the same side as the ___variable__. This is done by doing the
___opposite____. In most cases the ___inequality__ __symbol____ is simply
copied over.

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4.2 A cont’d
There is one situation in which solving a simple inequality is not as simple as solving
a simple equation. If both sides of an inequality are multiplied or divided by a
___negative___ number, the ___inequality__ __symbol____ is ____inverted
(flipped)____.

4.4A
Illustrating Compound Inequalities
A compound inequality is an inequality that combines two simple
__inequalities___ with either an “and” or an “or.” These compound inequalities
can be described with words, algebraic expressions, and graphs. The following table
shows how the words, the algebraic expressions, and the graphs are three ways to
describe the very __same____ thing. When graphing inequalities, the complete
number line is not necessary. Only endpoints need to be labeled. For your
convenience, these partial number lines have been provided for you. The first three
have been done for you. Note: An open circle [ ] denotes “not included” and a
closed circle denotes “included” [ ].

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Chapter 4 Review Name _________________________________

Complete the following table:

Inequality Words Graph
1)

x is greater than or equal
to −2

2)
4<x<8

3)

-4 -2 0 2 4
4)

x is less than 5

5)
x>4

6)
x is between −3 and 5

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Chapter 4 Review Name _________________________________
Solve each equation and graph the solution:

7) + 5 ≥ 2

8) 8 < −24

9) − 6 + ≤ −11

10) − 1 > −1
2

11) − 13 ≤ −9

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Chapter 4 Review Name _________________________________
Solve each equation and graph the solution:

12) −6 > 18

13) 2 + x < −3

14) ≥ −1
5

Solve these multi-step inequalities:
15) 3 + 3(2 + 1) > 5( − 5)

16) 2( + 12) + 6 ≥ 4(2 + 3)

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Chapter 4 Review Name _________________________________
Solve these multi-step inequalities:

17) 10( − 1) ≥ 7( + 2)

18) + 6( − 3) − 3 > 12( + 2)

Complete the table: Algebraic Expressions Graph

Words
19)

-6 2
2
20)
−2 < x < 4

21)
Numbers less than or
equal to −3 or greater than
5

22)
-4

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Chapter 4 Review Name _________________________________
23) x < −1 or x > 3

24)
Numbers between 2 and 6

Solve these compound inequalities and then graph the solutions:
25) −8 < 4 + 12 < 36

26) 3 + 7 ≤ 1 8 − 11 ≥ 29

27) −20 < 7 − 6 < 29

28) 7 − 9 < −2 3 + 4 > 34

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Chapter 4 Review Name _________________________________

Solve these compound inequalities and then graph the solutions:

29) 7< 1 + 8 < 10
2

30) 2 + 8 ≤ 14 5 − 15 ≥ 20

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Key Vocabulary Chapter Five

5.1A
• sequence
• term
• common difference

(d)
• successive term
5.2
• ordered pair
• coordinate
• relation
• set
• mapping diagram
• domain
• range
5.2B
• function
5.5A
• function notation

o y = ax
o f(x) = ax
• 5.6A
• scatterplot
• correlation
o positive
o negative
o none
5.7A
• Slant
• Slope
• steepness

1|Page

CHAPTER 5

Section One of Chapter 5 covers arithmetic sequences and relations and functions – both
demonstrate relationships. Arithmetic sequences show the relationship between
numbers while relations and functions show the relationship within ordered pairs of
numbers.
Section Two of Chapter 5 describes the various ways to represent these groups of
ordered pairs of numbers: list, t-chart, mapping diagram and graphs. After identifying
ordered pairs, it is necessary to identify the elements in the domain and range and
determine whether or not the relationship is a function or not.
Section three of Chapter 5 covers plotting and interpreting graphs as one way to
represent sets of ordered pairs is with a graph. Students will observe graphs and identify
the type of correlation (positive, negative, or none) that the data points demonstrate.
Finally, to enhance understanding of how a graph models relationships between two
variables, students will sketch graphs involving real-life situations.

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Chapter Five
Section One – Relationships

Arithmetic Sequences.............................................................................................................................5.1A

Quiz ..................................................................................................................................................5.1D

Relations and Functions

Relations .......................................................................................................................................5.2A

Functions ....................................................................................................................................... 5.2B

Quiz ................................................................................................................................................. 5.2E

Section Two – Function Notation

Function Equations .................................................................................................................................5.3A

Quiz ..................................................................................................................................................5.3D

Variable Relationships (Independent and Dependent) .........................................................5.4A

Quiz ..................................................................................................................................................5.4D

Function Notation (F(x)) ......................................................................................................................5.5A

Quiz ..................................................................................................................................................5.5D

Section Three – Interpreting Graphs

Graphing, Correlations, and Scatterplots......................................................................................5.6A

Quiz ..................................................................................................................................................5.6D

Sketching and Interpreting Graphs .................................................................................................5.7A

Exploration: Creating Story-Graphs -- Sketching Real World Scenarios

(Appendix)...................................................................................................................................................5.7D

Quiz .................................................................................................................................................. 5.7E

Cloze Responses

Chapter Review and Chapter Test

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