# Elementary and Intermediate Algebra by M. Dugopolski

By M. Dugopolski

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Extra info for Elementary and Intermediate Algebra

Sample text

5 b) The integers between 3 and 9 are 4, 5, 6, 7, and 8. Note that 3 and 9 are not considered to be between 3 and 9. The graph is shown in Fig. 6. 6 c) The integers greater than Ϫ3 are Ϫ2, Ϫ1, 0, 1, and so on. To indicate the continuing pattern, we use three dots on the graph shown in Fig. 7. Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 ... 1 The Real Numbers 5 U4V The Real Numbers For every rational number there is a point on the number line. For example, the 1 5 number ᎏᎏ corresponds to a point halfway between 0 and 1 on the number line, and Ϫᎏᎏ 2 4 corresponds to a point one and one-quarter units to the left of 0, as shown in Fig.

19 The notation Ϳ a Ϳ represents distance, and distance is never negative. So Ϳ a Ϳ is greater than or equal to zero for any real number a. E X A M P L E 6 Finding absolute value Evaluate. 39 Ϳ Solution a) Ϳ 3 Ϳ ϭ 3 because 3 is three units away from 0. b) Ϳ Ϫ3 Ϳ ϭ 3 because Ϫ3 is three units away from 0. c) Ϳ 0 Ϳ ϭ 0 because 0 is zero units away from 0. 39 Now do Exercises 47–54 Two numbers that are located on opposite sides of zero and have the same absolute value are called opposites of each other.

5. 5 b) The integers between 3 and 9 are 4, 5, 6, 7, and 8. Note that 3 and 9 are not considered to be between 3 and 9. The graph is shown in Fig. 6. 6 c) The integers greater than Ϫ3 are Ϫ2, Ϫ1, 0, 1, and so on. To indicate the continuing pattern, we use three dots on the graph shown in Fig. 7. Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 ... 1 The Real Numbers 5 U4V The Real Numbers For every rational number there is a point on the number line. For example, the 1 5 number ᎏᎏ corresponds to a point halfway between 0 and 1 on the number line, and Ϫᎏᎏ 2 4 corresponds to a point one and one-quarter units to the left of 0, as shown in Fig.