# Basic algebra Problems

Section 1.1 Exercises Pages 10-12 Problems 44, 48, 92, 98, 110

Write each interval of real numbers in interval notation and graph it.

44. The set of real numbers greater than or equal to _1 and less than 6

48. The set of real numbers less than or equal to _4

Consider the following nine integers: -4, -3, -2, -1, 0, 1, 2, 3, 4

92. Which of these integers has an absolute value greater than 1?

Write the interval notation for the interval of real numbers shown in each graph.

110. Discussion

Determine whether each number listed in the table below is a member of each set listed on the side of the table. For example, ½ is a real number and a rational number. So check marks are placed in those two cells of the table.

Section 1.2 Exercises Pages 22-24 Problems 18, 32, 80, 90, 92, 110

Build up each fraction or whole number so that it is equivalent to the fraction with the indicated denominator.

18. Reduce each fraction to lowest terms.

32. Convert each given fraction, decimal, or percent into its other two forms. See Example 8.

80. Find each sum or difference.

90.

92.

110. Diversification. Helen has 1/5 of her portfolio in U.S. stocks, 1/8 of her portfolio in European stocks, and 1/10 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds. What fraction of her portfolio is invested in municipal bonds? What percent is invested in municipal bonds?

3) Section 1.3 Exercises Pages 29-31 Problems 34, 62, 68, 88, 104

Fill in the parentheses to make each statement correct.

34. -9 - (-2.3) = -9 + (?)

Perform the indicated operations.

62. 44 - (-15)

68. 15 + (-39)

Fill in the parentheses so that each equation is correct.

88. 13 + ( ) = -4

104. Net worth. Melanie's house is worth $125,000, but she still owes $78,422 on her mortgage. She has $21,236 in a savings account and has $9,477 in credit card debt. She owes $6,131 to the credit union and figures that her cars and other household items are worth a total of $15,000. What is Melanie's net worth?

4) Section 1.4 Exercises Pages 34-35 Problems 42, 56, 70

Perform the indicated operations.

42. (-8) (-6)

56. -9/10 ? 4/3

Fill in the parentheses so that each equation is correct.

70. -48 ÷ ( ) = 6

5) Section 1.5 Exercises Pages 42-43 Problems 92, 114, 118, 126

Evaluate each expression.

92.

114. 8 - 3 │= 42 + 1

6) Section 1.6 Exercises Pages 49-52 Problems 66, 76, 102, 106

Evaluate each expression using a = -1, b = 2, and c = -3.

66.

Determine whether the given number is a solution to the equation following it.

76. 5, 3x - 7 = 2x + 1

102. Forensics. A forensic scientist uses the expression 72.6 + 2.5T to estimate the height in centimeters of a female with a tibia of length T centimeters. If a female skeleton has a tibia of length 32.4 cm, then what was the height of the person? Find the length of your tibia in centimeters, and use the expression from this exercise or the previous exercise to estimate your height.

106. Crop circles. The expression r2 gives the area of a circle with radius r. How many square meters of wheat were destroyed when an alien ship made a crop circle of diameter 25 meters in the wheat field at the Southwind Ranch? Find on your calculator.

7) Section 1.7 Exercises Pages 60-62 Problems 24, 42, 106

Use the commutative and associative properties of multiplication and exponential notation to rewrite each product. See Example 3.

24. y (y ∙ 5)( wy )

Use the distributive property to remove the parentheses. See Example 5.

42. - 3(6 - p)

106. Recovering golf balls. Susan and Joan are diving for golf balls in a large water trap. Susan recovers a golf ball every 0.016 hour while Joan recovers a ball every 0.025 hour. If both are working, then at what rate (in golf balls per hour) are they recovering golf balls?

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