Problem 1E: Give an example of each of the following: (a) A natural number (b) An integer that is not a natural... Problem 2E: Complete each statement and name the property of real numbers you have used. (a) ab = __________;... Problem 3E: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder... Problem 4E: The symbol | x | stands for the __________of the number x. If x is not 0, then the sign of | x | is... Problem 5E: The distance between a and b on the real line is d(a, b) = __________. So the distance between 5 and... Problem 6E: Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 6. (a) Is the sum of... Problem 7E: Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 7. (a) Is a b equal... Problem 8E: Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 8. (a) Is the... Problem 9E: Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c)... Problem 10E: Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c)... Problem 11E: Properties of Real Numbers State the property of real numbers being used. 11. 3 + 7 = 7 + 3 Problem 12E Problem 13E: Properties of Real Numbers State the property of real numbers being used. 13. (x + 2y) + 3z = x +... Problem 14E: Properties of Real Numbers State the property of real numbers being used. 14. 2(A + B) = 2A + 2B Problem 15E: Properties of Real Numbers State the property of real numbers being used. 15. (5x + 1)3 = 15x + 3 Problem 16E: Properties of Real Numbers State the property of real numbers being used. 16. (x + a)(x + b) = (x +... Problem 17E: Properties of Real Numbers State the property of real numbers being used. 17. 2x(3 + y) = (3 + y)2x Problem 18E: Properties of Real Numbers State the property of real numbers being used. 18. 7(a + b + c) = 7(a +... Problem 19E: Properties of Real Numbers Rewrite the expression using the given property of real numbers. 19.... Problem 20E Problem 21E: Properties of Real Numbers Rewrite the expression using the given property of real numbers. 21.... Problem 22E: Properties of Real Numbers Rewrite the expression using the given property of real numbers. 22.... Problem 23E Problem 24E Problem 25E: Properties of Real Numbers Use properties of real numbers to write the expression without... Problem 26E: Properties of Real Numbers Use properties of real numbers to write the expression without... Problem 27E: Properties of Real Numbers Use properties of real numbers to write the expression without... Problem 28E Problem 29E: Arithmetic Operations Perform the indicated operations. 29. (a) 310+415 (b) 14+15 Problem 30E: Arithmetic Operations Perform the indicated operations. 30. (a) 2335 (b) 1+5816 Problem 31E Problem 32E: Arithmetic Operations Perform the indicated operations. 32. (a) 223322 (b) 25+12110+315 Problem 33E: Inequalities Place the correct symbol (, , or =) in the space. 33. (a) 372 (b) 372 (c) 3.572 Problem 34E Problem 35E: Inequalities State whether each inequality is true or false. 35. (a) 3 4 (b) 3 4 Problem 36E: Inequalities State whether each inequality is true or false. 36. (a) 31.7325 (b) 1.73253 Problem 37E Problem 38E Problem 39E: (a) x is positive. (b) t is less than 4. (c) a is greater than or equal to . (d) x is less than 13... Problem 40E Problem 41E: Sets Find the indicated set if A=1,2,3,4,5,6,7B=2,4,6,8C=7,8,9,10 41. (a) A B (b) A B Problem 42E Problem 43E Problem 44E: Sets Find the indicated set if A=1,2,3,4,5,6,7B=2,4,6,8C=7,8,9,10 44. (a) A B C (b) A B C Problem 45E: Sets Find the indicated set if A=xx2B=xx4C=x1x5 45. (a) B C (b) B C Problem 46E Problem 47E: Intervals Express the interval in terms of inequalities, and then graph the interval. 47. (3, 0) Problem 48E: Intervals Express the interval in terms of inequalities, and then graph the interval. 48. (2, 8] Problem 49E: Intervals Express the interval in terms of inequalities, and then graph the interval. 49. [2, 8) Problem 50E Problem 51E: Intervals Express the interval in terms of inequalities, and then graph the interval. 51. [2, ) Problem 52E: Intervals Express the interval in terms of inequalities, and then graph the interval. 52. (, 1) Problem 53E: Intervals Express the inequality in interval notation, and then graph the corresponding interval.... Problem 54E Problem 55E: Intervals Express the inequality in interval notation, and then graph the corresponding interval.... Problem 56E Problem 57E Problem 58E Problem 59E: Intervals Express each set in interval notation. 59. (a) (b) Problem 60E: Intervals Express each set in interval notation. 60. (a) (b) Problem 61E: Intervals Graph the set. 61. (2, 0) (1, 1) Problem 62E: Intervals Graph the set. 62. (2, 0) (1, 1) Problem 63E: Intervals Graph the set. 63. [4, 6] [0, 8) Problem 64E Problem 65E: Intervals Graph the set. 65. (, 4) (4, ) Problem 66E: Intervals Graph the set. 66. (, 6] (2, 10) Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E: Absolute Value Evaluate each expression. 71. (a) | ( 2) 6| (b) (13)(15) Problem 72E Problem 73E Problem 74E Problem 75E: Distance Find the distance between the given numbers. 75. (a) 2 and 17 (b) 3 and 21 (c) 118and310 Problem 76E: (a) 715and121 (b) 38 and 57 (c) 2.6 and 1.8 Problem 77E: Repeating Decimal Express each repeating decimal as a fraction. (See the margin note on page 3.) 77.... Problem 78E Problem 79E Problem 80E Problem 81E: Simplifying Absolute Value Express the quantity without using absolute value. 81. |a b|, where a b Problem 82E Problem 83E: Signs of Numbers Let a, b, and c be real numbers such that a 0, b 0, and c 0. Find the sign of... Problem 84E Problem 85E: Area of a Garden Marys backyard vegetable garden measures 20 ft by 30 ft, so its area is 20 30 =... Problem 86E: Temperature Variation The bar graph shows the daily high temperatures for Omak, Washington, and... Problem 87E: Mailing a Package The post office will accept only packages for which the length plus the girth... Problem 88E: DISCUSS: Sums and Products of Rational and Irrational Numbers Explain why the sum, the difference,... Problem 89E: DISCOVER PROVE: Combining Rational and Irrational Numbers Is 12+2 rational or irrational? Is... Problem 90E: DISCOVER: Limiting Behavior of Reciprocals Complete the tables. What happens to the size of the... Problem 91E: DISCOVER: Locating Irrational Numbers on the Real Line Using the figures below, explain how to... Problem 92E: PROVE: Maximum and Minimum Formulas Let max(a, b) denote the maximum and min(a, b) denote the... Problem 93E: WRITE: Real Numbers in the Real World Write a paragraph describing different real-world situations... Problem 94E: DISCUSS: Commutative and Noncommutative Operations We have learned that addition and multiplication... Problem 95E: PROVE: Triangle Inequality We prove Property 5 of absolute values, the Triangle Inequality:... format_list_bulleted