Elementary Algebra Textbook
Solutions Manual
Second Edition
Department of Mathematics
,ii
Copyright
All parts of this prealgebra textbook are copyrighted Ⓧ
c 2011 in the
name of the Department of Mathematics, College of the Redwoods. They
are not in the public domain. However, they are being made available free
for use in educational institutions. This offer does not extend to any
application that is made for profit. Users who have such applications
in mind should contact David Arnold at or
Bruce Wagner at .
This work is licensed under the Creative Commons Attribution-Non-
Commercial-NoDerivs 3.0 Unported License. To view a copy of this li-
cense, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ or send
a letter to Creative Commons, 171 Second Street, Suite 300, San Fran-
cisco, California, 94105, USA.
, Contents
1 The Arithmetic of Numbers 1
1.1 An Introduction to the Integers ....................................................... 1
1.2 Order of Operations .............................................................................. 7
1.3 The Rational Numbers .................................................................... 18
1.4 Decimal Notation ................................................................................ 33
1.5 Algebraic Expressions .......................................................................... 47
2 Solving Linear Equations 53
2.1 Solving Equations: One Step .............................................................. 53
2.2 Solving Equations: Multiple Steps ...................................................... 60
2.3 Solving Equations: Clearing Frations and Decimals ....................... 73
2.4 Formulae.............................................................................................. 81
2.5 Applications ......................................................................................... 91
2.6 Inequalities ........................................................................................ 108
3 Introduction to Graphing 127
3.1 Graphing Equations by Hand........................................................ 127
3.2 The Graphing Calculator ............................................................... 140
3.3 Rates and Slope................................................................................. 149
3.4 Slope-Intercept Form of a Line ......................................................... 157
3.5 Point-Slope Form of a Line ........................................................... 168
3.6 Standard Form of a Line ............................................................... 183
4 Systems 205
4.1 Solving Systems by Graphing ....................................................... 205
4.2 Solving Systems by Substitution................................................... 226
4.3 Solving Systems by Elimination .................................................... 243
4.4 Applications of Linear Systems .................................................... 259
5 Polynomials 269
5.1 Functions ........................................................................................... 269
iii
, iv CONTENTS
5.2 Polynomials ........................................................................................ 280
5.3 Applications of Polynomials ............................................................. 290
5.4 Adding and Subtracting Polynomials ............................................ 298
5.5 Laws of Exponents ............................................................................ 303
5.6 Multiplying Polynomials ................................................................ 309
5.7 Special Products ................................................................................ 317
6 Factoring 335
6.1 The Greatest Common Factor .......................................................... 335
6.2 Solving Nonlinear Equations ............................................................. 347
6.3 Factoring Trinomials I ................................................................ 362
6.4 Factoring Trinomials II ............................................................... 378
6.5 Special Forms ..................................................................................... 397
7 Rational Functions 413
7.1 Negative Exponents ........................................................................... 413
7.2 Scientific Notation ............................................................................. 425
7.3 Simplifying Rational Expressions ................................................... 433
7.4 Solving Rational Equations ............................................................ 441
7.5 Direct and Inverse Variation ............................................................. 456
8 Quadratic Functions 465
8.1 Introduction to Radical Notation .................................................. 465
8.2 Simplifying Radical Expressions .................................................... 471
8.3 Completing the Square ...................................................................... 479
8.4 The Quadratic Formula ................................................................. 494
Second Edition: 2012-2013
Solutions Manual
Second Edition
Department of Mathematics
,ii
Copyright
All parts of this prealgebra textbook are copyrighted Ⓧ
c 2011 in the
name of the Department of Mathematics, College of the Redwoods. They
are not in the public domain. However, they are being made available free
for use in educational institutions. This offer does not extend to any
application that is made for profit. Users who have such applications
in mind should contact David Arnold at or
Bruce Wagner at .
This work is licensed under the Creative Commons Attribution-Non-
Commercial-NoDerivs 3.0 Unported License. To view a copy of this li-
cense, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ or send
a letter to Creative Commons, 171 Second Street, Suite 300, San Fran-
cisco, California, 94105, USA.
, Contents
1 The Arithmetic of Numbers 1
1.1 An Introduction to the Integers ....................................................... 1
1.2 Order of Operations .............................................................................. 7
1.3 The Rational Numbers .................................................................... 18
1.4 Decimal Notation ................................................................................ 33
1.5 Algebraic Expressions .......................................................................... 47
2 Solving Linear Equations 53
2.1 Solving Equations: One Step .............................................................. 53
2.2 Solving Equations: Multiple Steps ...................................................... 60
2.3 Solving Equations: Clearing Frations and Decimals ....................... 73
2.4 Formulae.............................................................................................. 81
2.5 Applications ......................................................................................... 91
2.6 Inequalities ........................................................................................ 108
3 Introduction to Graphing 127
3.1 Graphing Equations by Hand........................................................ 127
3.2 The Graphing Calculator ............................................................... 140
3.3 Rates and Slope................................................................................. 149
3.4 Slope-Intercept Form of a Line ......................................................... 157
3.5 Point-Slope Form of a Line ........................................................... 168
3.6 Standard Form of a Line ............................................................... 183
4 Systems 205
4.1 Solving Systems by Graphing ....................................................... 205
4.2 Solving Systems by Substitution................................................... 226
4.3 Solving Systems by Elimination .................................................... 243
4.4 Applications of Linear Systems .................................................... 259
5 Polynomials 269
5.1 Functions ........................................................................................... 269
iii
, iv CONTENTS
5.2 Polynomials ........................................................................................ 280
5.3 Applications of Polynomials ............................................................. 290
5.4 Adding and Subtracting Polynomials ............................................ 298
5.5 Laws of Exponents ............................................................................ 303
5.6 Multiplying Polynomials ................................................................ 309
5.7 Special Products ................................................................................ 317
6 Factoring 335
6.1 The Greatest Common Factor .......................................................... 335
6.2 Solving Nonlinear Equations ............................................................. 347
6.3 Factoring Trinomials I ................................................................ 362
6.4 Factoring Trinomials II ............................................................... 378
6.5 Special Forms ..................................................................................... 397
7 Rational Functions 413
7.1 Negative Exponents ........................................................................... 413
7.2 Scientific Notation ............................................................................. 425
7.3 Simplifying Rational Expressions ................................................... 433
7.4 Solving Rational Equations ............................................................ 441
7.5 Direct and Inverse Variation ............................................................. 456
8 Quadratic Functions 465
8.1 Introduction to Radical Notation .................................................. 465
8.2 Simplifying Radical Expressions .................................................... 471
8.3 Completing the Square ...................................................................... 479
8.4 The Quadratic Formula ................................................................. 494
Second Edition: 2012-2013
