82 Chapter 1 Linear Equations and Inequalities in One Variable Solution: We require that L 6 6. L d 7.2 0.05d 6 6 7.2 0.05d Substitute for L. Subtract 7.2 from both sides. Divide both sides by 0.05 and reverse the direction of the inequality sign. 7.2 7.2 0.05d 6 6 7.2 0.05d 6 1.2 0.05d 0.05 7 1.2 0.05 d 7 24 The water level in the pond will be less than 6 ft after day 24 of the drought. Skill Practice 6. The population of Alaska has steadily increased since 1950 according to the equation P 10t 117 , where t represents the number of years after 1950 and P represents the population in thousands. For what years since 1950 was the population less than 417 thousand people? Answer 6. The population was less than t 6 30 417 thousand for . This corresponds to the years before 1980. Section 1.4 Practice Exercises Study Skills Exercise Look over the notes that you took today. Do you understand what you wrote? If there were any rules, definitions, or formulas, highlight them so that they can be easily found when studying for the test.You may want to begin by highlighting the rule indicating when the direction of an inequality sign must be reversed. Vocabulary and Key Concepts 1. a. A relationship of the form is called a in one variable. ax b 7 c or ax b 6 c 1a 02 b. When solving an inequality, the direction of the inequality sign must be reversed when multiplying or dividing both sides of the inequality by a number. c. Which inequality statement represents the set of real numbers greater than 2? x 7 2 or 2 6 x Review Exercises 2. When using interval notation is it proper to use a parenthesis or a bracket with and ? For Exercises 3–8, complete the table. 4 ( 10 Set-Builder Notation Interval Notation Graph 3. 4. 5. 6. 7. 8. 13, 6 4 30, 42 5x 0 x 7 56 5x 0 x 26
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