Chapter 2 Review Exercises 185 40. When solving linear inequalities, we can multiply or divide both sides by a number and not change the relationship between the two expressions. 41. When solving linear inequalities, we can multiply or divide both sides by a number, but we must CHAPTER 2 / REVIEW EXERCISES SECTION 2.1 Determine whether each of the following is an expression or an equation. (See Objective 1.) 1. 7x - 9 = 2x - 12 2. -5r 2 + 11 - 12r - 24 3. 5x - 11 - 2x + 3 4. 6y2 - 10 = 12y - 5 Determine if the given numbers are solutions of the equation. Organize the information in tables. (See Objective 2.) 5. Is x = -4, x = -1, x = 0, x = 4, or x = - 4 5 a solution of 3x - 1 = -2x - 5? 6. Is x = -6, x = -2, x = 0, x = 3, or x = 1 2 a solution of x2 + 3x = 18? Assign a variable to the unknown quantity and then write an equation that represents each statement. (See Objective 3.) 7. Four times the sum of a number and -17 is the same as twice the number. Find the number. 8. The sum of a number and 18 is the same as seven times the number. Find the number. 9. The difference of four times a number and -3 equals 45 less than the number. Find the number. 10. One angle is 6° more than another angle. Their sum is 90°. Find the measure of each angle. 11. One angle is 17° less than another angle. Their sum is 180°. Find the measure of each angle. 12. From June 2008 to June 2009, John Mars and Larry Page were the two of the 31 richest Americans. Their combined net worth was $26.3 billion. John Mars’s net worth is $4.3 billion less than Larry Page’s. Find the net worth of each person. (Source: http:// www.forbes.com/lists/) SECTION 2.2 Solve each equation. (See Objectives 2 and 3.) 13. 5x + 6 = 2x + 18 14. 3 - x = 11 - 5x 15. 3 5 x + 2=-6 - 2 5 x 16. 4 7 - x = 5x - 3 7 17. 5(x - 2) + 13 = 3(x - 2) - 9 18. 1.24x + 3.25 = 2.94x - 1 19. 3.5x - 2.6 + 1.9x = 7.3x - 13.24 20. 32 - 10x = 32 - 15x also the inequality symbol to maintain the relationship between the two expressions. 42. The phrase “is at most” can be translated by the symbol . The phrase “is at least” can be translated by the symbol . For each problem: (1) assign a variable to the unknown, (2) write an equation that represents the situation, (3) solve the equation, and (4) answer the question using complete sentences. (See Objective 4.) 21. The sum of a number and -18 is the same as five times the number. Find the number. 22. Three times the sum of a number and 4 is the same as twice the number. Find the number. 23. Twice the difference of a number and -5 is the same as four times the number. Find the number. 24. Six more than a number is -1. Find the number. 25. The difference of twice a number and -19 is equal to 47 more than the number. Find the number. 26. One angle is 24° more than another angle. Their sum is 90°. Find the measure of each angle. 27. From June 2008 to June 2009, Christy Walton and Philip Knight were the two of the 31 richest Americans. Their combined net worth was $31 billion. Christy Walton’s net worth is $12 billion more than Philip Knight’s. Find the net worth of each person. (Source: http://www.forbes.com/ lists/) 28. From June 2008 to June 2009, Dr. Phil McGraw and Oprah Winfrey were the two of the top 100 celebrities. Their combined earnings were $355 million. Dr. Phil McGraw earned $195 million less than Oprah Winfrey. How much did each of them earn? (Source: http://www.forbes .com/lists/) SECTION 2.3 Solve each equation. (See Objectives 1 and 2.) 29. 5y - 7 = 23 30. -2x + 30 = 4x 31. a 2 =-8 32. 8z + 5 - 2z = 15 - 3z 33. -10x + 9 - 3x = 18 + 5x - 16 34. - 1 2 (x + 6) + 8 = x + 5 35. -1.8b + 6 = 42 36. -0.6y + 15.2 = 2.7y + 24.44 37. 1.2(5.2x - 3.2) = -0.6(2.5x - 0.05) 38. 12(x - 2) = 2(6x - 1) For each problem: (1) assign a variable to the unknown, (2) write an equation that represents the situation, (3) solve the equation, and (4) answer the question using complete sentences. (See Objectives 3 and 4.) 39. Three times a number is equal to -54. Find the number. 40. Two-fifths of a number is 12. Find the number.
hendricks_beginning_intermediate_algebra_1e_ch1_3
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