Introduction to Algebra links & errata

Below are some of the links that are referenced in the book Introduction to Algebra. (Note: Art of Problem Solving is not responsible for the content on any external site.)

How to Use This Book

Game of Life Links

Chapter 8

Chapter 9

Chapter 15

Chapter 17

Chapter 18

Unfortunately, the book is not perfect. Here is a list of the known errors. If you know of an error not on this list, we would appreciate a short email to books@artofproblemsolving.com describing the error.

First Edition Text:

• Chapter 3, page 70 and 72. Problem 3.15, second sentence should begin, "A pink pill costs $1 more than a green pill,"
• Chapter 5, Problem 5.19, page 130: The line for x=1 should be A+B = C+D, and the line for x=2 should be 2A+B = 2C+D.
• Chapter 8, Problem 8.8, page 202: The second sentence below the last pair of graphs should read, "If y_2 - y_1 and x_2 - x_1 are both positive, then y_2 is greater than y_1 and x_2 is greater than x_1."
• Chapter 10, Problem 10.14, page 284: All instances of the variable y should be z.
• Chapter 11, Problem 11.14, page 321: The second and third factorizations at the top of the page should be (x-2)(x^2 +2x+2^2) and (x-3)(x^2+3x+3^2)
• Chapter 13, page 371. Problem 13.11, in finding the root, the numerator should be -(-5), so the root is 12/5, not -12/5.
• Chapter 17, page 482. There's a very subtle error here. The graph of y=f(2x-1) is the graph of y=f(2x) shifted to the right by 1/2 unit, not 1 unit. (Try a few points and see why!)
• Chapter 20, Problem 20.9, page 549: Towards the end of the solution, there are two places where the book uses the expression |x+3| + |x-2|. Both should be |x-3|+|x+2|.
• Chapter 20, Problem 20.21, page 564: Case 2 should be -3-7x<0, not 3-7x<0.
• Chapter 21, Problem 21.10, page 582: In the third line of "Solution 1", the equation a_1 = a_4 + 3d should be a_4 = a_1 + 3d.
• Chapter 21, page 588. The exponent in the denominator in part (c) should be n, not n+1.

First Edition Solutions:

• Chapter 8, Problem 8.51. a=0 is also a solution.
• Chapter 11, Problem 11.5.4. The problem specified that the unit fractions are distinct, so we must exclude 1/12 + 1/12. The answer is 4.
• Chapter 16, Problem 16.2.2(b). The 16sqrt(2) should be 4sqrt(2).
• Chapter 17, Problem 17.2.1. The same subtle error in page 482 of the text exists in the solution for the graph of y=f(2x+3). The graph should be a horizontal compression by a factor of 1/2 followed by a leftward shift of 3/2 unit.
• Chapter 17, Problem 17.30. The same subtle error in page 482 of the text exists here, as well. The correct answer is that the graph of f(2-x) is the result of shifting the graph of f(x) to the left 2 units, and then reflecting the resulting graph over the y-axis.
• Chapter 17, Problem 17.33. The correct answer is 4, as there is a point to the right of the shown graph where the two graphs again intersect.
• Chapter 20, Problem 20.25(a). The domain is all real numbers greater than or equal to 3/2.

Second Edition Text:

• Chapter 1, Problem 1.35, page 45: The sentence should read "Therefore, sqrt(n) cannot be simplified if n is not divisible by any perfect square besides 1, but sqrt(n) can be simplified if n is divisible by a perfect square besides 1."
• Chapter 5, Problem 5.19, page 149: The line for x=1 should be A+B = C+D, and the line for x=2 should be 2A+B = 2C+D.
• Chapter 8, Problem 8.8, page 221: The second sentence below the last pair of graphs should read, "If y_2 - y_1 and x_2 - x_1 are both positive, then y_2 is greater than y_1 and x_2 is greater than x_1."
• Chapter 10, Problem 10.14, page 303: All instances of the variable y should be z.
• Chapter 11, Problem 11.14, page 340: The second and third factorizations at the top of the page should be (x-2)(x^2 +2x+2^2) and (x-3)(x^2+3x+3^2)
• Chapter 17, Problem 17.7, page 494: In the first two lines after the first centered equation in part (b), the pair (-4,-1) should be replaced with (-4,4). (The error is in two places.)
• Chapter 17, Problem 17.11, page 501: In step 2, we are scaling away from the x-axis, not the y-axis.
• Chapter 20, Problem 20.9, page 567: Towards the end of the solution, there are two places where the book uses the expression |x+3| + |x-2|. Both should be |x-3|+|x+2|.
• Chapter 20, Problem 20.21, page 582: Case 2 should be -3-7x<0, not 3-7x<0.
• Chapter 21, Problem 21.10, page 600: In the third line of "Solution 1", the equation a_1 = a_4 + 3d should be a_4 = a_1 + 3d.

Second Edition Solutions:

• Chapter 1, Problem 1.7.3(d). The answer is 1/16; a negative sign is mistakenly left out of the exponent.
• Chapter 16, Problem 16.2.2(b). The 16sqrt(2) should be 4sqrt(2).
• Chapter 20, Problem 20.25(a). The domain is all real numbers greater than or equal to 3/2.