Section 1.1 Introduction to Algebra and the Set of Real Numbers 51 3. Inequalities The relative size of two real numbers can be compared using the real number line. Suppose a and b represent two real numbers.We say that a is less than b, denoted a 6 b, if a lies to the left of b on the number line. a b a 7 b, a b We say that a is greater than b, denoted if a lies to the right of b on the number line. b a b a Table 1-1 summarizes the relational operators that compare two real numbers a and b. Mathematical Expression Translation Example a 6 b 2 6 3 a is less than b. a is greater than b. a is less than or equal to b. a is greater than or equal to b. a is equal to b. a is not equal to b. a 7 b 5 7 1 a b 4 4 a b 10 9 a b 6 6 a b 7 0 a b a is approximately equal to b. 2.3 2 Table 1-1 6, 7, , , The symbols and are called inequality signs, and the statements a 6 b, a 7 b, a b, a b, a b Table 1-2 and are called inequalities. Ordering Real Numbers Example 6 The average temperatures (in degrees Celsius) for selected cities in the United States and Canada in January are shown in Table 1-2. City Temp (C) Prince George, British Columbia 12.5 Corpus Christi, Texas 13.4 Parkersburg,West Virginia 0.9 San Jose, California 9.7 Juneau, Alaska 5.7 New Bedford, Massachusetts 0.2 Durham, North Carolina 4.2 Plot a point on the real number line representing the temperature of each city. Compare the temperatures between the following cities, and fill in the blank with the appropriate inequality sign: 6 or 7. Skill Practice Fill in the blanks with the appropriate inequality sign: 6 or 7. 14. 11 20 15. 3 6 16. 0 9 17. 6.2 1.8 Classroom Example: p. 57, Exercise 48 Answers 14. 6 15. 7 16. 7 17. 6
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