Chapters 1 and 2 Cumulative Review Exercises 145 CUMULATIVE REVIEW EXERCISES / CHAPTERS 1 AND 2 Determine the requested information about the given sets. (Section 1.1, Objective 1) 1. Use the roster method to write the set: B = {x | x is an integer strictly between -6 and 5} 2. Use the roster method to write the set: A = {x | x is a natural number less than 2π} Classify each real number as natural, whole, integer, rational, or irrational. List each classification that applies. (Section 1.1, Objective 2) 3. 12 2 3 4. -117 5. -8.901 6. 116 Graph each real number on the real number line. (Section 1.1, Objective 3) 7. 120 8. 4.3 Find the opposite of the given number. Assume a and b represent positive real numbers. (Section 1.1, Objective 4) 9. 5a 10. -24b Simplify each absolute value expression. (Section 1.1, Objective 5) 11. -|-43| 12. |-62| Perform the indicated operation. (Section 1.2, Objectives 1 and 2) 13. 5.1 + (-8.6) 14. 6.3 + (-14.9) 15. 1 6 + a- 5 6 b 16. 9 5 + a- 2 5 b 17. 24 ÷ a- 1 4 b 18. 12 0 19. (-13.5)(-10) 20. (-42)(5) Use the order of operations to simplify each expression. (Section 1.2, Objectives 3 and 4) 21. -6(-1)3 -10(-2)2 + 18 22. 6 -(15 - 7) - (1 - 3) - 32 ÷ 8 · 2 19 - 2127 - 2 23. 2u2 - 3u2 24. - 23 + 35 10-(-8) 25. - 4 - a- 7 5 b Evaluate each expression for the given values. (Section 1.2, Objective 5) 26. 2x2 - 5x + 1 for x = -3 27. -x3 + 4x - 7 for x = 2 28. b2 - 4ac for a = 6, b = -3, c = 1 29. 15x - 10y for x = 4, y = 0 Find both the additive inverse and multiplicative inverses of each number. (Section 1.3, Objective 1) 30. 12 31. -4 Apply the commutative, associative, or distributive properties to rewrite the given expression as an equivalent expression. (Section 1.3, Objective 2) 32. 14a - 8 33. (6 - x) + 2y 34. 23(m)n 35. -2(15x - 3y + 2) Simplify each expression. (Section 1.3, Objective 3) 36. -3x(10 + 2x) + 12x2 - 2(5x - 3) 37. 2 3 x + 7- 1 3 x + 17 38. 4 3 x + 1 - 1 5 x + 1 2 39. 5(2x + 6) - 2(x - 14) Translate each phrase or sentence into an algebraic expression, equation, or inequality. Use the variable x to represent the unknown number. (Section 1.3, Objective 4) 40. One-third the sum of a number and 13 41. Six more than twice a number is less than the number plus ten Solve each problem. (Section 1.3, Objective 5) 42. Jacob has collected 120 quarters and dimes. If x represents the number of dimes he collected, write an expression for the number of quarters he collected. 43. Referring to Exercise 42, if Jacob’s coins total $24, write an algebraic expression that represents the total value of his coins. Determine if the equation is a linear equation. If it is a linear equation, determine if x = -2 is a solution of the equation. (Section 2.1, Objective 1) 44. -4x -3 = 5 45. 2m2 + 7 = 15 Use the addition property of equality to solve each linear equation and check your answer. (Section 2.1, Objective 2) 46. 19 - d = 12.2 47. x - 5 = 7 Use the multiplication property of equality to solve each linear equation and check your answer. (Section 2.1, Objective 3) 48. a 13 =3 49. 3x = 24
hendricks_intermediate_algebra_1e_ch1_3
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