330 CHAPTER 6 Algebra, Graphs, and Functions Devon is currently taking Sociology and needs to earn a course grade of B to maintain his scholarship. Devon has taken 4 tests and is about to take his fifth and final test. Devon would like to know what range of grades on this last test would give him a grade of B in the course. In this section, we will see how we can use a linear inequality to represent this and many other everyday problems. Solving Linear Inequalities SECTION 6.5 LEARNING GOALS Upon completion of this section, you will be able to: 7 Solve a linear inequality. 7 Solve compound inequalities. Why This Is Important Linear inequalities can be used to represent many problems that we face in our everyday lives. The problems we will see in this section involve employee salaries, college employment, parking fees, business profit, and many other financial applications. Understanding how to model and solve such problems using algebra is a very powerful tool. We first discussed inequalities in Section 5.2 when we discussed the integers. In this section, and in the rest of the textbook, when we use inequalities, we will be working with the set of real numbers. The symbols of inequality are as follows. Symbols of Inequality a b < means that a is less than b. a b ≤ means that a is less than or equal to b. a b > means that a is greater than b. a b ≥ means that a is greater than or equal to b. Challenge Problems/Group Activities 61. Photography An article in the magazine Outdoor and Travel Photography states, “If a surface is illuminated by a point-source of light, the intensity of illumination produced is inversely proportional to the square of the distance separating them. In practical terms, this means that foreground objects will be grossly overexposed if your background subject is properly exposed with a flash. Thus direct flash will not offer pleasing results if there are any intervening objects between the foreground and the subject.” If the subject you are photographing is 4 ft from the flash and the illumination on this subject is 1 16 of the light of the flash, what is the intensity of illumination on an intervening object that is 3 ft from the flash? 1 9 62. Water Cost In a specific region of the country, the amount of a customer’s water bill, W, is directly proportional to the average daily temperature for the month, T, the lawn area, A, and the square root of F, where F is the family size, and inversely proportional to the number of inches of rain, R. In one month, the average daily temperature is 78°F and the number of inches of rain is 5.6. If the average family of four who has a thousand square feet of lawn pays $72.00 for water for that month, estimate the water bill in the same month for the average family of six who has 1500 ft2 of lawn. $132.27 $ Gorodenkoff/123RF
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