CHAPTER 5 Solving First Degree Equations in One Variable
5.8 Chapter Review
Review Exercises
Verify a Solution of an Equation
In the following exercises, determine whether each number is a solution to the equation.
| 1. | 2. |
| 3. | 4. |
Solve Equations using the Subtraction and Addition Properties of Equality
In the following exercises, solve each equation using the Subtraction Property of Equality.
| 5. | 6. |
| 7. | 8. |
In the following exercises, solve each equation using the Addition Property of Equality.
| 9. | 10. |
| 11. | 12. |
In the following exercises, solve each equation.
| 13. | 14. |
| 15. | 16. |
Solve Equations That Require Simplification
In the following exercises, solve each equation.
| 17. | 18. |
| 19. | 20. |
Translate to an Equation and Solve
In the following exercises, translate each English sentence into an algebraic equation and then solve it.
| 21. Four less than is 13. | 22. The sum of and is 25. |
Translate and Solve Applications
In the following exercises, translate into an algebraic equation and solve.
| 23. Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh? | 24. Rochelle’s daughter is 11 years old. Her son is 3 years younger. How old is her son? |
| 25. Elissa earned $152.84 this week, which was $21.65 more than she earned last week. How much did she earn last week? | 26. Peter paid $9.75 to go to the movies, which was $46.25 less than he paid to go to a concert. How much did he pay for the concert? |
Solve Equations Using the Division and Multiplication Properties of Equality
In the following exercises, solve each equation using the division and multiplication properties of equality and check the solution.
| 27. | 28. |
| 29. | 30. |
| 31. | 32. |
| 33. | 34. |
| 35. | 36. |
| 37. | 38. |
Solve Equations That Require Simplification
In the following exercises, solve each equation requiring simplification.
| 39. | 40. |
| 41. | 42. |
Translate to an Equation and Solve
In the following exercises, translate to an equation and then solve.
| 43. The quotient of b and and 9 is . | 44. 143 is the product of and y. |
| 45. The difference of s and one-twelfth is one fourth. | 46. The sum of q and one-fourth is one. |
Translate and Solve Applications
In the following exercises, translate into an equation and solve.
| 47. Janet gets paid $24 per hour. She heard that this is of what Adam is paid. How much is Adam paid per hour? | 48. Ray paid $21 for 12 tickets at the county fair. What was the price of each ticket? |
Solve an Equation with Constants on Both Sides
In the following exercises, solve the following equations with constants on both sides.
| 49. | 50. |
| 51. | 52. |
Solve an Equation with Variables on Both Sides
In the following exercises, solve the following equations with variables on both sides.
| 53. | 54. |
| 55. | 56. |
Solve an Equation with Variables and Constants on Both Sides
In the following exercises, solve the following equations with variables and constants on both sides.
| 57. | 58. |
| 59. | 60. |
Solve Equations Using the General Strategy for Solving Linear Equations
In the following exercises, solve each linear equation.
| 61. | 62. |
| 63. | 64. |
| 65. | 66. |
| 67. | 68. |
| 69. | 70. |
| 71. | 72. |
Classify Equations
In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.
| 73. | 74. |
| 75. | 76. |
Solve Equations with Fraction Coefficients
In the following exercises, solve each equation with fraction coefficients.
| 77. | 78. |
| 79. | 80. |
| 81. | 82. |
Solve Equations with Decimal Coefficients
In the following exercises, solve each equation with decimal coefficients.
| 83. | 84. |
Use the Distance, Rate, and Time Formula
In the following exercises, solve.
| 85. Mallory is taking the bus from Edmonton to North Battleford. The distance is 300 miles and the bus travels at a steady rate of 60 miles per hour. How long will the bus ride be? | 86. Natalie drove for hours at 60 miles per hour. How much distance did she travel? |
| 87. Link rode his bike at a steady rate of 15 miles per hour for hours. How much distance did he travel? | 88. Aaron’s friend drove him from Williams Lake to Kamloops. The distance is 187 miles and the trip took 2.75 hours. How fast was Aaron’s friend driving? |
Solve a Formula for a Specific Variable
In the following exercises, solve.
| 89. Use the formula. to solve for a) when when and b) in general |
90. Use the formula. to solve for t a) when and b) in general |
| 91. Use the formula to solve for a) when and b) in general |
92. Use the formula to solve for a) when and b) in general |
| 93. Solve the formula for y a) when b) in general |
94. Use the formula to solve for the principal, P for a) ,, b) in general |
| 95. Solve the formula for . | 96. Solve for . |
Everyday Math
| 97. Describe how you have used two topics from this chapter in your life outside of your math class during the past month. |
Review Exercises Answers
| 1. no | 3. yes |
| 5. | 7. |
| 9. | 11. |
| 13. | 15. |
| 17. | 19. |
| 21. | 23. 161 pounds |
| 25. $131.19 | 27. |
| 29. | 31. |
| 33. | 35. |
| 37. | 39. |
| 41. | 43. |
| 45. | 47. $32 |
| 49. | 51. |
| 53. | 55. |
| 57. | 59. |
| 61. | 63. |
| 65. | 67. |
| 69. | 71. |
| 73. contradiction; no solution | 75. identity; all real numbers |
| 77. | 79. |
| 81. | 83. |
| 85. 5 hours | 87. 37.5 miles |
| 89. a); b) | 91. a)b) |
| 93. a)b) | 95. |
Practice Test
Determine whether each number is a solution to the equation .
| 1. a) 5 b) |
In the following exercises, solve each equation.
| 2. | 3. |
| 4. | 5. |
| 6. | 7. |
| 8. | 9. |
| 10. | 11. |
| 12. | 13. |
| 14. | 15. |
| 16. | 17. |
| 18. | 19. |
| 20. | 21. Solve the formula for y a) when b) in general |
| 22. Samuel paid $25.82 for gas this week, which was $3.47 less than he paid last week. How much had he paid last week? |
Practice Test Answers
| 1. a) yes b) no | 2. |
| 3. | 4. |
| 5. | 6. |
| 7. | 8. |
| 9. | 10. |
| 11. | 12. |
| 13. | 14. |
| 15. | 16. |
| 17. | 18. |
| 19. contradiction; no solution | 20. |
| 21. a) b) | 22. |
Attributions
This chapter has been adapted from “Review Exercises” and “Practice Test” in Chapter 2 of Elementary Algebra (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.