Section 2.8 Linear Inequalities 175 Translating Expressions Involving Inequalities Example 9 Write the English phrases as mathematical inequalities. a. Claude’s annual salary, s, is no more than $40,000. b. A citizen must be at least 18 years old to vote. (Let a represent a citizen’s age.) c. An amusement park ride has a height requirement between 48 in. and 70 in. (Let h represent height in inches.) Solution: a. Claude’s annual salary, s, is no more than $40,000. b. A citizen must be at least 18 years old to vote. c. An amusement park ride has a height requirement between 48 in. and 70 in. s 40,000 a 18 48 6 h 6 70 Skill Practice Write the English phrase as a mathematical inequality. 13. Bill needs a score of at least 92 on the final exam. Let x represent Bill’s score. 14. Fewer than 19 cars are in the parking lot. Let c represent the number of cars. 15. The heights, h, of women who wear petite size clothing are typically between 58 in. and 63 in., inclusive. Linear inequalities are found in a variety of applications. Example 10 can help you determine the minimum grade you need on an exam to get an A in your math course. Solving an Application with Linear Inequalities Example 10 To earn an A in a math class, Alsha must average at least 90 on all of her tests. Suppose Alsha has scored 79, 86, 93, 90, and 95 on her first five math tests. Determine the minimum score she needs on her sixth test to get an A in the class. Solution: Let x represent the score on the sixth exam. Label the variable. Create a verbal model. Simplify. Multiply both sides by 6 to clear fractions. Solve the inequality. Subtract 443 from both sides. Interpret the results. a 90 Average of all tests b 79 86 93 90 95 x 443 x 6 443 x 6 90 90 b 19026 443 x 540 x 540 443 x 97 6a 6 Alsha must score at least 97 on her sixth exam to receive an A in the course. Skill Practice 16. To get at least a B in math, Simon must average at least 80 on all tests. Suppose Simon has scored 60, 72, 98, and 85 on the first four tests. Determine the minimum score he needs on the fifth test to receive a B. Answers 13. x 92 14. c 6 19 15. 58 h 63 16. Simon needs at least 85. The average score is found by taking the sum of the test scores and dividing by the number of scores.
miller_beginning_intermediate_algebra_4e_ch1_3
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