Master
Math:
Algebra
Debra

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P.O. Box 687
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0 1996 by

book
by
by

MASTER MATH: ALGEBRA
by
by

VISA

on

Library of Congress Cataloging-in-PublicationData

/ by

:

p.
)

1.
1996
5

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Acknowledgments

Dr.

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Table of Contents

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Introduction

1

Chapter 1 Translating Problems into
Algebraic Equations

5

1.1.
1.2.

5

1.3.
1.4.

6
8
12

Chapter 2 Simplifying Algebraic Equations

22

2.1.
22
2.2.

23
26

2.3.

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by

2.4.

28
2.5.
30

Chapter 3 Solving Simple
Algebraic Equations

31

3.1.
31
3.2.
39
3.3.

43

Chapter 4 Algebraic Inequalities

46

4.1.
46

Chapter 5 Polynomials

49

5.1.
5.2.
5.3.
5.4.
5.5.
5.6.

49
51
52
53
55
61

5.7.
62

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Chapter 6 Algebraic Fractions with
Polynomial Expressions
6.1.
6.2.
6.3.
6.4.

72
72
73
74
76

Chapter 7 Solving Quadratic Polynomial
Equations with One Unknown
Variable

81

7.1
82

7.2
83
7.3
87
7.4

90

7.5.
92

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Chapter 8 Solving Systems of Linear
Equations with Two or Three
Unknown Variables
8.1.

95

of

96
8.2.

98

8.3.
103
8.4.

105
8.5.
110
8.6.

111
8.7.

115
8.8.

119
8.9.

126

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Chapter 9 Working with Coordinate Systems
and Graphing Equations
9.1.
9.2.
9.3.
9.4.
9.5.
9.6.
9.7.

133
134
139
145
150

152
155
160

9.8.
164

on

Index

169

Appendix Tables of Contents of First and
Third Books in the Mwter Math
Series

172

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Introduction

Algebra

ter Math
Basic Math and Re-Algebra
metry.
Master Math

MasPre-Calculus and Geo-

book

Algebra

Algebra

book

Algebra

Algebra

1
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Algebra

book
on
on
book

Master Math

Algebra

Master

Math
no

Muster Math
book

A

2
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Introduction

“I do

up.

3
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Chapter 1

Translating Problems
intoAlgebraic Equations
1.1
1.2
1.3
1.4

1.1. Introduction to algebra

you
you

$20.00
you

$1.00
you

5
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buy


Algebra

“X.”

$1.00
$20.00?

you
$20.00.
$20.00.

x

$1.00
by $1.00

=

1.2. Translating English into
algebraic equations

by
added
to, plus, sum, in all, altogether, increased by, the sum of,
more, total.
by
difference,how many less, subtracted from, how many
more, reduced by, decreased by, minus, less, take away.
6
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Translating Problems into Algebraic Equations

by
multiplied by, of, times, product, multiply, twice
by 2), double
by 2 ) .
by
divided by, quotient, divides, ratio.
2nd

squared

cubed

by
equals, is equal, is, are, were, was, the sum is, the
difference is, the quotient is, the product is, the same as,
results in, the result is, makes, leaves, yields, gives.
by
a number, what.

38

8

an unknown, a variable,

3
x

3x + 8 = 38.
11.

5
y

(2y)2 - 5 = 11.

5
n

of
5 + n3 = 13.
7
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13.


Algebra

1.3. Algebra terminology

A

Letters
by

b,

A,

x, y, z,

A variable

by x, y, z,

A
d,

b,

n,

constants.
by
or by

coeficient.
3y,

3

y
-4

8
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x


Translating Problems into Algebraic Equations

=3 * n

3n =

2*3#23

As
expression

numerical

x4y

algebraic expression.

An equation

up

An

9
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Algebra

+, -

=

by

+

terms.
no
3x

2x

3

2.2.

9x, 6

2x,
2x.

by

Inequalities

on
on
>, <, 2

I,

.

10
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Translating Problems into Algebraic Equations

factors

= 18x,

x

x

=

x2,

x

18

x

Polynomials
no
“1”

4x4 - 2x2 + 4
45x2 3x + 9
-8

+

5.1.

Linear equations
do

1.
2x

+ 1= 5
x

A,

Ax
y

+

=C ,

y=
b
y

on

9 on

11
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+ b,


Algebra

Non-Linear equations
1.
1= 5

1.4. Simple word problems

Important note:
2,

3,

Perimeter Word Problems

1,
book
Master Math
and Geometry

Be-CaZcuZus
2

3
2

4

+3

+4

=9

4

6
2(4

+

+ 12

=8

12
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= 20


Translating Problems into Algebraic Equations

Area Word Problems

1,
book
Master Math
CaZcuZus and Geometry

Pre-

=

=

3
2

(3

=6

Volume Word Problems

book
Pre-CaZcuZus and Geometry

=

13
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1,
Master Math


Algebra

3

2

4
= 24

(3

Price and Profit Word Problems

=

- (%

=

$24

$24 = $X - (0.25)($~)
x=
$24 = $x(l $24 = $x(0.75)
= $X

$x = $32
$32 i s
2

=

3

-

14
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