336 CHAPTER 6 Algebra, Graphs, and Functions Exercises Warm Up Exercises In Exercises 1–8, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A statement containing two or more expressions joined by an inequality symbol is called a(n) _______. Inequality 2. a) a b < means that a is _______ than b. Less b) a b > means that a is _______ than b. Greater 3. An inequality of the form a x b < < is called a(n) _______ inequality. Compound 4. When solving an inequality, if you obtain a statement that is always false, such as > 3 5, the answer is _______ solution. No 5. When solving an inequality, if you obtain a statement that is always true, such as > 2 1, the solution is _______ real numbers. All 6. When both sides of an inequality are multiplied or divided by a(n) _______ number, the direction of the inequality symbol is reversed. Negative 7. To indicate the solution set of x 5 ≤ on the number line, we draw a(n) _______ circle at 5 and a line to the left of the circle. Closed 8. To indicate the solution set of x 5 < on the number line, we draw a(n) _______ circle at 5 and a line to the left of the circle. Open Practice the Skills In Exercises 9– 46, solve the inequality, and graph the solution set on the number line. 9. x 4 ≥ * 10. x 3 < * 11. x 5 > * 12. x 2− ≥ * 13. x 9 4 + ≥ * 14. x 11 3 + ≤ * 15. x 5 8 − < − * 16. x 8 9 − > − * 17. x6 36 − ≤ * 18. x4 12 − < * 19. x 3 3 − ≥ * 20. x 2 4 − ≤ − * 21. x2 6 14 + ≥ * 22. x3 7 5 − < * 23. x5 3 12 − + < − * 24. x3 7 22 − + > * 25. x x 2 5 4 25 − + ≤ − * 26. x x 3 12 5 14 + < + * 27. x x 3(2 1) 4(2 1) 3 + > − + * 28. x x 2(3 4) 9( 1) 8 − < + − * 29. x x 4(2 1) 2(4 3) − < − * 30. x x x 3 7 6( 1)3( 1) − + ≥ − − + + * 31. x x 5(2 7) 2(5 4) − ≤ + * 32. x x x 3 11 6( 2) 3( 4) + ≥ + − + * 33. + > − x x 8 9 8 27 1 3 7 27 * 34. + > − x x 1 2 9 12 1 3 1 12 * 35. x 1 3 − ≤ ≤ * 36. x 4 1 − < ≤ * 37. x 2 4 6 < − ≤ * 38. x 8 5 2 − ≤ + < * 39. x 7 3 2 8 − < + ≤ * 40. x 3 2 5 11 − ≤ + < * 41. x 1 2 4 2 4 < + ≤ * 42. x 3 3 2 1 2 − ≤ − < * 43. x 3 2 1 3 1 − ≤ − < * 44. x 1 2 3 5 1 − ≤ + ≤ * 45. < + ≤ x 1 3 3 6 3 2 * 46. − ≤ − < x 3 4 1 8 1 2 * Problem Solving 47. U.S. Motor Vehicle Production The following graph was created using StatCrunch with data obtained from the U.S. Bureau of Transportation website (BTS.gov). The graph shows the total vehicle production, in millions of vehicles, in the United States for the years 2014–2021. 0 2 4 6 8 10 12 14 11.2 11.3 9.2 2014 2015 2016 2017 2018 2019 2020 2021 Year Number of Vehicles (millions) U.S. Motor Vehicle Production 11.7 12.1 12.2 10.9 8.8 Source: BTS.gov In which years was the number of vehicles produced a) 12 million? > 2015, 2016 b) 10 million? < 2020, 2021 c) 10 million > and 12 million? < 2014, 2017, 2018, 2019 d) 8 < million? None SECTION 6.5 *See Instructor Answer Appendix
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