By James Stewart, Lothar Redlin, Saleem Watson
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Extra resources for Algebra and Trigonometry (3rd Edition)
The absolute value of a quotient is the quotient of the absolute values. 12 CHAPTER P | Prerequisites What is the distance on the real line between the numbers Ϫ2 and 11? From Figure 10 we see that the distance is 13. We arrive at this by finding either 0 11 Ϫ 1Ϫ22 0 ϭ 13 or 0 1Ϫ22 Ϫ 11 0 ϭ 13. From this observation we make the following definition (see Figure 11). 13 _2 | b-a | 0 11 a FIGURE 10 b F I G U R E 1 1 Length of a line segment is 0 b Ϫ a 0 DISTANCE BETWEEN POINTS ON THE REAL LINE If a and b are real numbers, then the distance between the points a and b on the real line is d1a, b2 ϭ 0 b Ϫ a 0 From Property 6 of negatives it follows that 0 b Ϫ a 0 ϭ 0 a Ϫ b 0 .
The positive direction (toward the right) is indicated by an arrow. We choose an arbitrary reference point O, called the origin, which corresponds to the real number 0. Given any convenient unit of measurement, each positive number x is represented by the point on the line a distance of x units to the right of the origin, and each negative number Ϫx is represented by the point x units to the left of the origin. Thus every real number is represented by a point on the line, and every point P on the line corresponds to exactly one real number.
31–32 48. 1Ϫ2, 0 2 പ 1Ϫ1, 1 2 51. 1Ϫq, Ϫ4 2 ʜ 14, q 2 Write each statement in terms of inequalities. 27. (a) A ʜ B 2 49. 3Ϫ4, 64 പ 3 0, 82 25. (a) (b) (c) (d) (e) ■ 0 47. 1Ϫ2, 02 ʜ 1Ϫ1, 12 0 27–30 −3 −2 1 47–52 ■ 5 0 (b) 24. 25–26 0 Find the inequality whose graph is given. 0 23. −3 46. (a) 21. 22. Express each set in interval notation. 45. (a) 18. x Ͼ Ϫ4 19. x Ͻ Ϫ3 ■ 45–46 Omak, WA Geneseo, NY 80 75 70 65 Sun Mon Tue Wed Day Thu Fri Sat 14 CHAPTER P | Prerequisites 64. Fuel Consumption Suppose an automobile’s fuel consumption is 28 mi/gal in city driving and 34 mi/gal in highway driving.