Translating and Solving a Compound Inequality Example 12 The sum of a number and 4 is between 5 and 12. Find all such numbers. Solution: Let x represent a number. Translate the inequality. Subtract 4 from all three parts of the inequality. 5 6 x 4 6 12 5 4 6 x 4 4 6 12 4 The number may be any real number between 9 and 8: Skill Practice 17. The sum of twice a number and 11 is between 21 and 31. Find all such numbers. 5x 0 9 6 x 6 86. 9 6 x 6 8 Answer 17. Any real number between 5 and 10: 5n 0 5 6 n 6 106 TIP: • In mathematics, the word “between” means strictly between two values. That is, the endpoints are excluded. Example: x is between 4 and 10 1 (4, 10). • If the word “inclusive” is added to the statement, then we include the endpoints. Example: x is between 4 and 10, inclusive 1 4, 10. Section 1.5 Practice Exercises Study Skills Exercise Which activities might you try when working in a study group to help you learn and understand the material? Quiz one another by asking one another questions. Practice teaching one another. Share and compare class notes. Support and encourage one another. Work together on exercises and sample problems. Vocabulary and Key Concepts 1. a. The of two sets A and B, denoted by , is the set of elements that belong to A or B or both A and B. b. The of two sets A and B, denoted by , is the set of elements common to both A and B. c. The solution set to the compound inequality x c and x d is the (union/intersection) of the solution sets of the individual inequalities. d. The compound inequality a x and x b can be written as the three-part inequality . e. The solution set to the compound inequality x a or x b is the (union/intersection) of the solution sets of the individual inequalities. Section 1.5 Compound Inequalities 93
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