Algebra for College Students by Mark Dugopolski

By Mark Dugopolski

Algebra for students, 5e is a part of the newest choices within the winning Dugopolski sequence in arithmetic. The author’s objective is to provide an explanation for mathematical suggestions to scholars in a language they could comprehend. during this ebook, scholars and school will locate brief, specified factors of phrases and ideas written in comprehensible language. the writer makes use of concrete analogies to narrate math to daily studies. 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 of a math booklet, the writer has paid shut recognition to crucial info for fixing the given subject. Dugopolski incorporates a double cross-referencing method among the examples and workout units, so regardless of which one the scholars commence with, they're going to see the relationship to the opposite. ultimately, the writer reveals it very important not to in basic terms supply caliber, but in addition an excellent volume of workouts and purposes. The Dugopolski sequence is understood for offering scholars and school with the main volume and caliber of routines in comparison 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 fundamental info each pupil must turn into winning in destiny arithmetic classes.

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3 In This Section 2 ᎏᎏ, 99 Operations on the Set of Real Numbers Computations in algebra are performed with positive and negative numbers. In this section, we will extend the basic operations of arithmetic to the negative numbers. U1V Absolute Value U2V Addition U3V Subtraction U4V Multiplication U5V Division U6V Division by Zero U1V Absolute Value The real numbers are the coordinates of the points on the number line. 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.

45. 47. 49. AʕN ͕2, 3͖ ʕ C B C лʕB Aʕл AʝBʕC 40. 42. 44. 46. 48. 50. BʕN CʕA C A лʕC Bʕл B ʝ C ʕ ͕2, 4, 6, 8͖ U5V Combining Three or More Sets Using the sets D, E, and F, list the elements in each set. If the set is empty write л. See Example 6. D ϭ ͕3, 5, 7} E ϭ {2, 4, 6, 8} F ϭ ͕1, 2, 3, 4, 5͖ 51. D ʜ E 52. D ʝ E List the elements in each set. 65. ͕x Ϳ x is an even natural number less than 20͖ 66. ͕x Ϳ x is a natural number greater than 6͖ 67. ͕x Ϳ x is an odd natural number greater than 11͖ 68.

Using the sets A, B, C, and N, determine whether each statement is true or false. Explain. See Example 1. 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, . ͖ 7. 3 ʦ A 9. 11 A 8. 3 ʦ B 10. qxd 10/31/07 6:37 PM Page 8 8 1-8 Chapter 1 The Real Numbers 11. C ϭ N 13. A B 15. 99 ʦ N 12. A ϭ N 14. C N 16. 6 ʦ C U2–3V Union and Intersection of Sets Using the sets A, B, C, and N, list the elements in each set. If the set is empty write л. See Examples 2 and 3. 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, .

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