Introductory Algebra

Reviewed by Eunju Park, Developmental Math Faculty, Montana State University Bozeman on 4/13/25

Comprehensiveness rating: 4 see less

The textbook covers all areas and concepts in introductory algebra. While it is designed to be easy for students to understand, index and glossary are not provided in the book.

Content Accuracy rating: 4

There are several mistakes throughout the textbook. For instance, there is a misleading explanation on book page 129: x(−1) > 4(−1) in Line 15 followed by −x < −4 in Line 16. These two statements are contradictory and may only increase students’ confusion. Many more identified errors (not intended to be entirely comprehensive) are noted in the comments section below.

Relevance/Longevity rating: 5

Information and content are up-to-date. It does a great job explaining various concepts in a thematically and conceptually connected manner.

Clarity rating: 4

Although I see strengths in the structure of the textbook organization where it appears to follow the natural flow of students’ thinking, it lacks rigorous definitions of terms and supporting proofs at times.

Consistency rating: 5

The introduction of each concept and the process are consistent.

Modularity rating: 5

The modules are well-organized and easy to divide into small sections. There are lots of practice problems and summaries for students and teachers, as a good resource.

Organization/Structure/Flow rating: 5

The topics are well-organized and clearly provided. It appears to start by building on students’ background knowledge.

Interface rating: 5

The diagrams, charts, and tables are clear. For instance, the colorful and vivid geometric figures on PP. 58-61, PP. 68-71 make the explanations easier to digest for students. Furthermore, provided video links & QR code links seem helpful for the students to better understand the concepts.

Grammatical Errors rating: 4

There are several typos throughout the textbook.

Cultural Relevance rating: 5

The text is not culturally insensitive or offensive.

Comments

* The pages below are the pages of the pdf file, not the textbook page.
Page 16: Line 16 where a Rule is described in words (Rule: To subtract a number, add its opposite).
The following would be helpful to add: For any real numbers a and b, a+(−b) = a-b.
Page 17: Line 13
Ex2 The word “start” is at the wrong place.
Page 24: Line 7
“m=1/5” and units are missing.
Page 32: Line 18
Typo: The answer correct is 13.
Page 41: Line 9
Typo: EVALUATE 7y−11, when y = 4.
Page 43: “In 27 – 31, evaluate the real-life problems.” should be in the following line, line 22. Typo: In 28, not In27
Page 56: Line 7, 9, 12, 13, 14, 15
x should be changed to “x”. i.e. from normal alphabetical letter to mathematical letter
Page 56: Line 13 and 19
Example 4b), Simplify -4(3x - 2) didn’t match the solution.
Page 60: Line 1-2
The link is not working. http://www.quia.com/ba/2 8820.html.
Page 62: Line 3
Typo: ….which will will ….
Page 62: Line 12-14
There are definitions of exponent, base, and power. There is no definition of the exponential form or notation.
Page 79: Line 15, Page 82: Line 11 and 14
Typo: (a) x 10 x 5 = χ 10−5 = χ 5. It looks like Chi.
Page 82: Line 19
The video link is not working. - http://tinyurl.com/7n3ae2l
Page 88: Line 6
Typo: double periods
Page 99: Line 1-2
one-step equations of the form y = ax and two-step equations of the form y = ax+b
The form should be ax = some number or ax+b = some number, not function notations.
Page 113: Line 7
0.3786×100 = 37.86%. It’s mathematically incorrect. 0.3786×100% = 37.86%
Page 115: Line 15
−0.3% should be changed to -0.3.
Page 124: Line 29 (last line)
(-∞,1/2} => (-∞,1/2] Use a bracket.
Page 125: Line 9
“If x < a, then x−c < a−c” should be changed to “If x > a, then x+b > a+b.”
Page 129: Line 15 and 16
x(−1) > 4(−1)
−x < −4
The two statements are contradictory. The concept should be explained differently.
Page 129: Line 24
The moment you divide by a negative number, the direction of the inequality must change.
Page 130: Line 4
Typo: It’s interval notation, not set notation.
Page 130: Line 6
http://khanexercises.appspot.com/video?v=PNXozoJWsWc. The video link is not working.
The QR code is linked to an unrelated topic.
Page 130: Line 11
The link, CK-12 Basic Algebra:Inequalities Using Multiplication and Division is working, but the QR code is linked to an unrelated topic.
Page 132: Line 15
Typo: Example 1: Solve for w : 6x−5 < 10. It should be “ Solve for x.”
Page 136: Line 3
The QR code is linked to an unrelated topic.
Page 143: Line 8
The link, http://tinyurl.com/72myodv is not working.
Page 147: Line 3
The word, “FIGURE 8.1” should be removed or hidden.
Page 149: Line 23
There are two graphs. The gray colored graph should be removed.
Page 154: Line
Typo: ”the rate of charge” should be “the rate of change.”
Page 171: Line 30 (last line)
Range: All whole numbers. The range should be all even non-negative integers.
Page 172: Line 12, P173: Line 20, P181: Line 10
The link is working, but the QR code is linked to an unrelated topic.
Page 183: Line 4 and 11
There are no problems numbers, 8 and 9.
Page 192: Line 17
The link is working, but the QR code is linked to an unrelated topic.
Page 195: Line 9
Typo: The truck covers no distance for 2 hours, not 1 hour.
Page 201: Line 12 and 13
There should be one graph in Example 4 a).
There should be one graph in Example 4 b).
Page 204: Line 14 and 15
Both the link, thttp://standards.nctm.org/document/eexamples/chap7/7.5/index.htm. http://tinyu rl.com/7laf6oh and the QR code are not working.
Page 219: Line 12 and 16
Both the link and the QR code are not working.
Page 224:
The link is working, but the QR code is not working.
Page 226: Line 7
Typo: you must remember, not must be remember.
Page 245: Line 12 and Line 13
Typo: The system of the equations should be the middle of the sentence.
Page 245: Line 14, 261: Line 22 and 23, Page 262: Line 5, Page 267 Line 24, Page 268 Line 6, Page 273: Line 16 - Line 39
They need to be lined up.
Page 255: Line 12
The variables a and b are not defined before being used.
Page 256: Line 29
Typo: “at” should be removed.
Page 262: Line 18 and 19
“amp” should be removed.
Reorder: amp; x+y = 90
Move “Multiply equation two by 2” before 2x+2y = 180
Page 263: Line 20
The link is working, but the QR code is not working.
Page 268: Line 10
Missing 3. 3x+3y = 9 not x+3y=9
Page 276: Line 5
Typo: From … so you to become a better problem solver.. to … so you can or would become a better problem solver.
Typos: There are many missing apostrophes.
Page 153: Line 11, Page 190: Line 12, Page 191: Line 8 and Line 10, - You’ll,
Page 194: Line 15, Page 195:Line 15, Page 203 Line 10, - We’ll
Page 199: Line 3 – doesn’t
Page 201: Line 2 – That’s
Page 204: Line 5 – can’t
Page 204: Line 8 – We’d
Typos: A space should be inserted.
Page 237: Line 9 - both equationsin other
Page 242: Line 7- slopeintercept
Page 249: Line 8 – useall, Line 25 - …a purchasefor
Page 259: Line 19 and 20 – denominatorthat, denominatorand

Reviewed by Samuel Chukwuemeka, Assistant Professor of Mathematics, Blue Ridge Community College on 10/7/24

Comprehensiveness rating: 3 see less

(1.) The book covers the required areas of Introductory Algebra.
However:
(2.) There is no index in the book.
(3.) There is no glossary in the book.
(4.) There is no in-text citation.
(5.) There are no references in the book.
(6.) Solutions to the Practice Set including the Problem Set and Review Questions (even for odd-numbered questions) were not provided.

Content Accuracy rating: 4

The content is accurate for the most part, however, there are contents that may affect the understanding of concepts.
For example: Typically, if variables are not defined before they are used in a program, the program will not run.
The same principle apply in Mathematics.

Examples:
It is important to define variables:
(1.) Page 102 (pdf page, not text page):
"3. Isolate the ax term."
(a.) What is a? What is x? What is the ax term?

(2.) Page 251 (pdf page, not text page):
What is n_1, n_2, V_1, V_2?

Relevance/Longevity rating: 4

The content is relevant and up-to-date.
However, necessary updates may not be relatively easy to implement.
One reason is because the solutions to the Problem Set, Practice Set, and Review Questions (even for odd-numbered questions) was not provided.
Another reason is because some necessary terms are missing. For example: in Page 7 (pdf page, not text page): A Whole number can also be defined as a nonnegative integer. The term, "nonnegative" is an important term.

Clarity rating: 4

The book is written in clear terms and is generally not difficult to comprehend.
However, the book does not meet accessibility standards.
(1.) Manually reviewing it for accessibility: Example: some link names do not describe the purpose/context of the information.
(2.) PDF accessibility checker: I used the DocAxess website: https://www.docaxess.com/en/homepage/ and the result is:
Status: This PDF file is not PDF/UA compliant.

Consistency rating: 5

In terms of terminology and framework, the writing style for each chapter of the book is the same.

Modularity rating: 3

It is noteworthy to mention that the Example and Solution are emphasized in bold.

However, these are my recommendations based on Modularity:
(1.) Leave enough spacing between each example and the corresponding solution.
(2.) Leave enough spacing between the solution of one example and the question of another example.
(3.) Leave enough spacing before each concept/subheading.
(4.) Leave enough spacing (at least 1.5) between each question in the Practice Set.
(5.) Leave enough spacing (at least 1.5) between each question in the Chapter Reviews.
(6.) Latex/MathJax/Math Equation Editor should be used for all Math terms including fractions among others.

Organization/Structure/Flow rating: 5

The topics in the book are presented in a clear, logical manner.

Interface rating: 3

It is remarkable to note that QR codes that lead to YouTube videos are embedded in the textbook.
This allows for students to view these videos on their mobile devices:
Please note that these are pdf pages (not textbook pages)
Pages 9, 11, 17, 18, 24, 26, 45, 52, 65, 80, 83, 93, 97, 100, 104, 109 114, 116, 126, 130, 136, 143, 172, 173, 181, 182, 204, 219, 224, 233, 295

Be it as it may, these features may confuse the reader.
Please note that these are pdf pages (not textbook pages)
Embedded Linked Image: Click image to the left for more content.
This leads to a blank page
In other words, these links do not work:

Pages:
9: https://www.ck12.org/flx/render/embeddedobject/9966
11: https://www.ck12.org/flx/render/embeddedobject/9967
17: https://www.ck12.org/flx/render/embeddedobject/9968
18: https://www.ck12.org/flx/render/embeddedobject/9969
24: https://www.ck12.org/flx/render/embeddedobject/9970
26: https://www.ck12.org/flx/render/embeddedobject/9971
45: https://www.ck12.org/flx/render/embeddedobject/9976
52: https://www.ck12.org/flx/render/embeddedobject/9977
65: https://www.ck12.org/flx/render/embeddedobject/9978
80: https://www.ck12.org/flx/render/embeddedobject/9979
83: https://www.ck12.org/flx/render/embeddedobject/9980
93: https://www.ck12.org/flx/render/embeddedobject/9981
97: https://www.ck12.org/flx/render/embeddedobject/9982
100: https://www.ck12.org/flx/render/embeddedobject/9983
104: https://www.ck12.org/flx/render/embeddedobject/9984
109: https://www.ck12.org/flx/render/embeddedobject/9985
114: https://www.ck12.org/flx/render/embeddedobject/9986
116: https://www.ck12.org/flx/render/embeddedobject/9987
126: https://www.ck12.org/flx/render/embeddedobject/9988
130: https://khanexercises.appspot.com/video?v=PNXozoJWsWc
136: https://www.ck12.org/flx/render/embeddedobject/9990
143: http://tinyurl.com/72myodv
(https://www.math-play.com/Coordinate%20Plane%20Game/Coordinate%20Plane%20Game.html).
143: https://www.ck12.org/flx/render/embeddedobject/9991
172: https://www.ck12.org/flx/render/embeddedobject/9992
173: https://www.ck12.org/flx/render/embeddedobject/9993
181: https://www.ck12.org/flx/render/embeddedobject/9994
182: https://www.ck12.org/flx/render/embeddedobject/9995
204: http://standards.nctm.org/document/eexamples/chap7/7.5/index.htm.
204: http://standards.nctm.org/document/eexamples/chap7/7.5/index.htm.http://standards.nctm.org/document/eexamples/chap7/7.5/index.htm.
219: https://www.ck12.org/flx/render/embeddedobject/9972
224: https://www.ck12.org/flx/render/embeddedobject/9973
233: https://www.ck12.org/flx/render/embeddedobject/9974
295: https://www.ck12.org/flx/render/embeddedobject/9975

Grammatical Errors rating: 4

There are few grammatical errors in the book such as:
(1st.) Spelling error: (at least 15 instances of spelling errors of Heres and Theres)
Pages: 153, 153, 154, 155, 156, 159, 190, 190, 200, 240, 241, 247, 255, 257, 271

(2nd.) Page 119: (pdf page, not textbook page)
Table 7.1: Simple Interest Formula
Incorrect spelling: "Princial"

Cultural Relevance rating: 5

The book is not culturally insensitive. It does not contain offensive writings.

Comments

As applicable, the hyphens used in the book could be misconstrued as subtraction operations rather than bullets.
For example: Page 131 (pdf page, not textbook page):
Numbers (24.) and (25.):
When applicable, it is better to use a colon rather than a hyphen.