92 Chapter 1 Linear Equations and Inequalities in One Variable Solving a Compound Inequality: Or Solve the compound inequality. or Solution: 4x 3 6 16 or 2x 6 3 or Solve each inequality separately. or x 7 4 6 ( ( 6 Take the union of the solution sets. 6 5 4 3 2 1 0 1 2 3 4 5 6 The union of the solution sets is { is a real number}, or equivalently, 1, 2. Skill Practice Solve the compound inequality. 14. x 7 7 2 or 6x 7 48 5. Applications of Compound Inequalities Compound inequalities are used in many applications, as shown in Examples 11 and 12. Translating Compound Inequalities Example 11 The normal level of thyroid-stimulating hormone (TSH) for adults ranges from 10.4 mU/mL2 to 4.8 microunits per milliliter ,inclusive. Let x represent the amount of TSH measured in microunits per milliliter. a. Write an inequality representing the normal range of TSH, inclusive. b. Write a compound inequality representing abnormal TSH levels. Solution: a. 0.4 x 4.8 b. x 6 0.4 or x 7 4.8 Skill Practice The length of a normal human pregnancy, w, is from 37 to 41 weeks, inclusive. 15. Write an inequality representing the normal length of a pregnancy. 16. Write a compound inequality representing an abnormal length for a pregnancy. x 0 x 5x 0 x 7 32 6 5 4 3 2 1 0 1 2 3 4 5 6 32 5x 0 x 6 13 6 5 4 3 2 1 0 1 2 3 4 5 6 13 4 3 2 x 6 13 4 x 7 3 2 4x 6 13 4x 3 6 16 2x 6 3 Example 10 Answers 14. is a real number 15. 16. w 6 37 or w 7 41 6; 1, 5x 0 x 2 37 w 41
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