Prealgebra and Introductory Algebra: An Applied Approach

1045 Pages·2013·168.6 MB·English

by  Richard N. Aufmann

65426_fm_i-xxx.indd 2 1/3/13 12:21 PM
Take AIM and Succeed!
AIM
Aufmann Interactive Method
The Aufmann Interactive Method (AIM) is a proven learning system that
has helped thousands of students master concepts and achieve results.
To follow the aim, step t2h96roCuHAgPThER 5t h Seol vHing EOquaWtionS TO
examples that are provided asnedct itohnen work through
5.2
the matched EXAMPLE / YOU TRGYen eIrTal Epqauiartsio.ns—Part I
  OBJECTIVE A To solve an equation of the form ax 1 b 5 c Aufmann
In solving an equation of the form ax1b5c, the goal is to rewrite the equation in the
form variable5constant. This requires the application of both the Addition and Multi-
plication Properties of Equations.
3
How to 1 Solve: 4x225211
The goal is to write the equation in the form variable5constant.
3
x225211
4
3
4x2212521112 • Add 2 to each side of the equation.
take Note
C 34h2ec1 34k2:x22225221111 43# 3434xx55243929 ••  SMimulptilpiflyy. each side of the equation by 43.
1 29222 211 x521122 • The equation is in the form variable5constant.
2115211
A true equation The solution is 212.
Here is an example of solving an equation that contains more than one fraction.
2 1 3
Interactive How to 2 SolSveE: 3Cx1TI2O5N4 5.2    General equations—Part i 299
2 1 3
x1 5
3 2 4
23x112212534212 • Subtract 12 from each side of the equation.
ExamplE 5 23x514 •  Simpliyfy.Ou Try IT 5
Solve: 2x1425x510 32 23x 532 14 •  MultiplSy oealchv esid:e  oxf th2e eq5uat1ion b4y x32.525
a b 3a b
S14 CHAPTER 5    x58
Solution Your solution
 2x1425x510 The solution is 38.
 23x14510   • Combine lIsitik dmee ao ytf betehr eem aesqiseur.a ttoio sno lbvye tahne e lqeuaastt ioconm comnotani nminuglt itpwloe o(Lr mCMor)e ofrfa tchtieo ndse nboym minualttioprlsy.i nFgo re athche
 23x14Y2ou4 5Tr1y0 It2 44   • Subtract 4e4 q fduriavotiidmoen e avebeaonvcleyh, itn hsteoi dLitC.e TM.h eorfe 3fo, r2e,, aifn db o4t hi ss i1d2e.s T ohf et hLeC eMqu hataiso nth aer ep rmopueltritpyl itehdYa tb y3o, 12u2,, a tnhTde ry It 2
2 7 denominators will divide evenly into 12. The result is an equation that does 5noxt co2ntain1 023x5624x
 23x5 6x135 any fractions. Multiplying each side of an equation that contains fractions by the LCM
3 2 of the denominators is called clearing denominators. It is an alternative method, as we 2 x2105624x • Combine like terms.
23x 6 show in the next example, of solving an equation that contains fractions.
 23 652x213 3  5• 6Div7ide each side by 23. 2x1 64xx221100556624x14x • Add 4x.
3 2
 x522 6x21011056110 • Add 10.
2a b a7b
The soluti 6on isx 2625412.6_Ch056_2833-336.ind5d 2966 • Distributive Property 12/3/12 611:3x6 AM516
3 2
6x 16
a b 4x11182 521a b 6Sol5ution6 on p. S14 • Divide by 6.
For extra support, y 4oxu1 c18an2 1fi8n5d 2t1h2e 1c8o m p• lSeutbetr ascot 1l8u.tions to 8
4x53 x5
the YOU TRY IT problem4sx in3 the back of the text. 3
4 54 • Divide by 4. The solution is 8.
Method 3
  OBJECTIVE B xT5o3 solve application problems using formulasYou Try It 3
4 5x24322x 523x22 16
ExamplTE h6e solution is 34. yOu Try IT 6 5x2 11132x21182x2 5566xx1 2142126 • Distributive Property
You Try It 5 x2514x525
To determine the total cost of production, an  The pressure at a certa 1in3 xde2pth6 xin2 the1 2oc5ean6 xca2n b6ex 12 • Subtract 6x.
economis t uses the  equation T5U 5x#2N155F, 25 approximated by the equation  7Px5211521512D, 
where T is  the total  cost, U is 5 txhe2 un5it1 co5st,5 N 2is5  15 where P is the pressure  7inx p2ou1n2ds1 pe1r 2sq5ua22re 1inc1h2  • Add 12.
the numbe r of units  made, and F is the  5fixxe5d c3o0st.  and D is the depth in feet. Use this eq 7uxa5tion1 4to 
Use this equation to find the number of5 uxnits 30 find the depth when the pressure is 45 pounds per 
made duri ng a mon th in which the total  5co5st w5as  square inch. 7x514 • Divide by 7.
$9000, the unit cost was $25, and the fixed cost  7 7
x56
was $3000. x52
The solution is 6.
The solution is 2.
Strategy Your strategy
You Try It 6
Given:  T59000 You Try It 4
   US5tra25tegy Given: P545 22 3x252x23 53x28
   F 53000 Unknown: D 22 3x210x115 53x28 • Distributive Property
Copyright 2013 Cengage LeUarnninkgn. Aolwl Rnig:h tNs Reserved. May not be copied, scanned, or duplicated, in w1hole or in part. Due to electronic rights, some third party conte3nt may be sup1pressed from2 t4he eBook and/or eChapter(s) .
Editorial review has deemed that any suppresseSd coonltuentt diooesn no t materially affect the ov Peral5l lear1ni5ng e1xperie nDce. Cengage Learning reserves the right to remove additional co 2nte2nt a2t an7y xtim1e if s1ub5sequ5ent r3igxhts2 restr8ictions require it.
2 3 14x230453x28
4551511 D 14x323x230453x23x28 •  Subtract 3x.
Solution 2 Your solution 11x230528
65426_IFC.indd 2  T5U#N1F 1 11x230130528130 •  Add1 23/208./12 9:29 AM
 900052 5N130 00    • 4T552901050, 5U515252, F155310002 D 11x522
 6000525N     • Subtract 3000 1from each side. 11x 22
305 D 5 •  Divide by 11.
6000 25N 2 11 11
  5 • Divide each side by 25.
25 25     1 x52
230 52# D
 2405N 2 The solution is 2.
There wer e 240 uni ts made. 1 602 5D
You Try It 5
The depth is 60 ft. Strategy SolutioGni ovne pn.: S1 F41545
F 580
SECTION 5.3 2
d525
You Try It 1 Unknown: x
5x1456110x
5x210x1456110x210x • Subtract 10x. Solution F1x5F2 d2x
45x580252x
25x1456
1 2
65426_Ch05_283-336.indd 299 25x14245624 • Subtract 4. 451x2/35/12 2 110:306 0AM280x
45x180x5200102802x180x
25x52
125x52000
25x 2
5 • Divide by 25. 125x 2000
25 25 5
125 125
2
x52 x516
5
The fulcrum is 16 ft from the
The solution is 225. 45-pound force.
65426_em-sol_S01-S42.indd 14 12/3/12 11:35 AM
Ask the Authors!
We have taught math for many years. During that time, we have Author Author
haandd sthtuisd ceonutsrs aes. kH uesr ea ynouum fibnedr soof mquee osft itohnes q aubeosutito mnsa twhee mhaavtiecs Courtesy of the Courtesy of the
been asked most often, starting with the big one.
Dick Aufmann Joanne Lockwood

Why do I have to take this course? You may have heard that “Math is everywhere.” That
is probably a slight exaggeration, but math does find its way into many disciplines. There are obvious places
like engineering, science, and medicine. There are other disciplines such as business, social science, and
political science where math may be less obvious but still essential. If you are going to be an artist, writer,
or musician, the direct connection to math may be even less obvious. Even so, as art historians who have
studied the Mona Lisa have shown, there is a connection to math. But, suppose you find these reasons not
all that compelling. There is still a reason to learn basic math skills: You will be a better consumer and
be able to make better financial choices for you and your family. For instance, is it better to buy a car or
lease a car? Math can provide an answer.
I find math difficult. Why is that? It is true that some people, even very smart people,
find math difficult. Some of this can be traced to previous math experiences. If your basic skills are lacking,
it is more difficult to understand the math in a new math course. Some of the difficulty can be attributed to
the ideas and concepts in math. They can be quite challenging to learn. Nonetheless, most of us can learn
and understand the ideas in the math courses that are required for graduation. If you want math to be less
difficult, practice. When you have finished practicing, practice some more. Ask an athlete, actor, singer,
dancer, artist, doctor, skateboarder, or (name a profession) what it takes to become successful and the one
common characteristic they all share is that they practiced—a lot.
Why is math important? As we mentioned earlier, math is found in many fields of study. There
are, however, other reasons to take a math course. Primary among these reasons is to become a better
problem solver. Math can help you learn critical thinking skills. It can help you develop a logical plan to solve
a problem. Math can help you see relationships between ideas and to identify patterns. When employers are
asked what they look for in a new employee, being a problem solver is one of the highest ranked criteria.

What do I need to do to pass this course? The most important thing you must do is to
know and understand the requirements outlined by your instructor. These requirements are usually given to
you in a syllabus. Once you know what is required, you can chart a course of action. Set time aside to study
and do homework. If possible, choose your classes so that you have a free hour after your math class. Use
this time to review your lecture notes, rework examples given by the instructor, and begin your homework.
All of us eventually need help, so know where you can get assistance with this class. This means know-
ing your instructor’s office hours, the hours of the math help center, and how to access available online
resources. And finally, do not get behind. Try to do some math EVERY day, even if it is for only 20 minutes.
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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Prealgebra and
edition
3
Introductory Algebra
An Applied ApproAch
richard n. Aufmann
Palomar College
Joanne S. lockwood
Nashua Community College
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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Prealgebra and Introductory Algebra: © 2014, 2009 Brooks/Cole, Cengage Learning
An Applied Approach, Third Edition
ALL RIGHTS RESERVED. No part of this work covered by the copyright herein
Richard N. Aufmann, Joanne S. Lockwood
may be reproduced, transmitted, stored, or used in any form or by any means,
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Brief Contents
 A 
   AIM for Success   AIM-1
  1 
   Whole Numbers   1
  2 
   Fractions and Decimals   79
  3 
   Rational Numbers   179
  4 
   Variable Expressions   249
  5 
   Solving Equations   283
  6 
   Proportion and Percent   337
  7 
   Geometry   391
  8 
   Statistics and Probability   459
  9 
   Polynomials   491
10 
   Factoring   535
11 
    Rational Expressions   585
12 
   Linear Equations in Two Variables   643
13 
   Systems of Linear Equations   697
14 
   Inequalities   739
15 
   Radical Expressions   771
16 
   Quadratic Equations   805
Final Exam   845
 T 
    Transitioning to Algebra   849
Appendix   879
Table of Geometric Formulas and Properties   886
Solutions to “You Try It”   S1
Answers to Selected Exercises   A1
Glossary   G1
Index   I1
v
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
65426_fm_i-xxx.indd 5 1/3/13 4:06 PM
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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