Algebra for College Students by Mark Dugopolski

By Mark Dugopolski

Algebra for students, 5e is a part of the most recent choices within the profitable Dugopolski sequence in arithmetic. The author’s objective is to provide an explanation for mathematical strategies to scholars in a language they could comprehend. during this booklet, scholars and school will locate brief, distinctive factors of phrases and ideas written in comprehensible language. the writer makes use of concrete analogies to narrate math to daily reviews. for instance, while the writer introduces the Commutative estate of Addition, he makes use of a concrete analogy that “the fee of a hamburger plus a Coke is equal to a Coke plus a hamburger”. Given the significance of examples inside a math ebook, the writer has paid shut awareness to crucial info for fixing the given subject. Dugopolski contains a double cross-referencing method among the examples and workout units, so regardless of which one the scholars commence with, they are going to see the relationship to the opposite. ultimately, the writer reveals it very important not to in simple terms offer caliber, but in addition a very good volume of routines and purposes. The Dugopolski sequence is understood for supplying scholars and college with the main volume and caliber of workouts compared to the other developmental math sequence out there. In finishing this revision, Dugopolski feels he has constructed the clearest and so much concise developmental math sequence out there, and he has performed so with out comprising the basic info each scholar must develop into winning in destiny arithmetic classes.

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Example text

2121121112 . . ʦ Q 38. 3333 . . ʦ Q 74. The set of real numbers between Ϫ1 and 1 inclusive 39. 252525 . . ʦ I 40. 1010010001 . . ʦ I 41. 999 . . ʦ I 42. 666 . . ʦ Q 43. ␲ ʦ I 44. ␲ ʦ Q Place one of the symbols ʕ, each statement is true. , ʦ, or W 46. Z Q 47. Z N 48. Q W 49. Q R 50. I 51. л I 52. л Q 53. N R 54. W R 55. 5 Z 56. Ϫ6 57. 7 Q 58. 8 61. 0 63. ͕2, 3͖ 65. ͕3, ͙2ෆ ͖ R 62. 0 I R 77. 3 4 5 6 7 8 9 78. 3 4 5 6 7 8 9 Q I Q 64. ͕0, 1͖ Q 76. The set of real numbers greater than 2 and less than or equal to 5.

D ʜ (E ʝ F) 60. D ʜ (F ʝ E ) 61. (D ʝ F) ʜ (E ʝ F) 62. (D ʝ E) ʜ (F ʝ E) 64. (D ʜ F) ʝ (D ʜ E) 17. A ʜ C 18. A ʜ B 63. (D ʜ E) ʝ (D ʜ F) 19. A ʝ C 21. B ʜ C 20. A ʝ B 22. B ʝ C Miscellaneous 23. A ʜ л 25. A ʝ л 27. A ʝ N 24. B ʜ л 26. B ʝ л 28. A ʜ N Use one of the symbols ʦ, , ϭ, , ʜ, or ʝ in each blank to make a true statement. See Example 4. A ϭ ͕1, 3, 5, 7, 9} B ϭ {2, 4, 6, 8} C ϭ ͕1, 2, 3, 4, 5͖ N ϭ ͕1, 2, 3, . ͖ 29. 30. 31. 32. 33. 34. 35. 37. AʝB л AʝC л A B ϭ ͕1, 2, 3, 4, 5, 6, 7, 8, 9͖ A Bϭл B C ϭ ͕2, 4͖ B C ϭ ͕1, 2, 3, 4, 5, 6, 8͖ 3 AʝB 36.

However, we often refer to the points as numbers. For example, the numbers 5 and Ϫ5 are both five units away from 0 on the number line shown in Fig. 28. A number’s distance from 0 on the number line is called the absolute value of the number. ” Therefore, Ϳ 5 Ϳ ϭ 5 and Ϳ Ϫ5 Ϳ ϭ 5. 28 E X A M P L E 1 Absolute value Find the value of Ϳ 4 Ϳ, Ϳ Ϫ4 Ϳ, and Ϳ 0 Ϳ. Solution Because both 4 and Ϫ4 are four units from 0 on the number line, we have Ϳ 4 Ϳ ϭ 4 and Ϳ Ϫ4 Ϳ ϭ 4. Because the distance from 0 to 0 on the number line is 0, we have Ϳ 0 Ϳ ϭ 0.

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