1. Algebraic Expressions and Variables

2. Problem Solving Analyze the problem. Define your variable. Form an equation. Solve the equation Check the solution State the conclusion

3. In order to form equations, we need to know how to translate words into mathematical expressions. In this section, we will learn how to do this.

4. Definition

5. Example Which of the following are expressions?

6. Translating Phrases that involve Addition The sum of 2 and x 2 + x 8 increased by 2 8 + 2 7 more than v v + 7 6 greater than x x + 6 Exceeds L by 20 L + 20

7. Translating Phrases that involve Subtraction The difference of 2 and y 2 - y c decreased by 2 c - 2 7 less than v v - 7 6 reduced by x 6 - x 20 less L 20 - L

8. Translating Phrases involving Multiplication

9. Translating Phrases involving Division

10. Translating the following phrases:

11. Definition

12. Evaluating Expressions

13. Example

16. Definition

17. Formula for Sales Price

18. Example

22. Examples

23. More Examples

24. The Distributive Property

25. Examples

27. More Examples

28. The Extended Distributive Property

29. Examples

30. The Right Hand Distributive Property

31. Examples

34. Similar Terms

35. BIG DEAL

36. Examples

37. More Examples

38. Using the Distributive Property

39. Examples

40. Using the Distributive Property

42. Multiplying by -1

43. Examples

44. More Examples

51. Problem Solving Analyze the problem. Define your variables. Form an equation. Solve the equation Check the solution State the conclusion

52. Suppose apples sell for 59 cents per pound. Find the cost of Five pounds of apples. x pounds of apples. M pounds of apples. (p - 2) pounds of apples

53. Example Suppose you want to construct a rectangular garden that has a perimeter of 600 feet. If the length is twice the width, what should the dimensions of the garden be?

54. Example After failing your first exam, you study really hard to improve your grade. On the second exam your score is 22 points more than the score on your first exam. If the total of your two exam scores is 144 points, what were your two test scores?

55. Example In a biology course, students spend a total of 250 minutes in lab and lecture each week. The amount of time spent in lab is 50 minutes shorter than the amount of time spent in lecture. How much time is spent in lecture each week?

56. Example A landscaper buried a water pipe around a rectangular-shaped lawn to serve as a supply line for a sprinkler system. The length of the lawn is 5 times its width. If 240 feet of pipe was used, what is the width of the lawn?

57. Example In an effort to cut costs, a company decided to lay off 5 employees every month until the number of employees totals 465. If 510 people are now employed, how long will it take to reach the employment goal?

58. Example A preschool charges $8 per child to attend the morning session, and $10 to attend the afternoon session. No child can attend both. Thirty children are enrolled in the preschool. If the daily receipts are $264, how many children attend each session?

59. Example At a service station, the underground tank that stores regular gas holds 100 gallons less than the tank that stores premium gas. If the total storage capacity of both tanks is 700 gallons, how much gas does each tank hold?

60. Example At noon, a passenger ship and a freighter left port traveling in opposite directions. By midnight, the passenger ship was 3 times farther from port than the freighter. If the distance between the two ships at midnight was 84 miles, How far was the freighter from the port?

61. Example A salesman receives a commission of $3 for every pair of dress shoes he sells. He receives a commission of $2 for every pair of athletic shoes he sells. After selling 9 pairs of shoes in one day, his commission was $24. How many pairs of each type of shoe did he sell?

62. Example After receiving a score of 95 and 85 on the first two exams in his math class, Joe skips one exam and gets a score of 0. What scores must he get on his last two tests to get a C in the course (70 average)?

63. Example For every problem answered correctly on an exam, 3 points are awarded. For every incorrect answer, 4 point are deducted. In a 10 question test, a student scored 16 points. How many correct and incorrect answers did the student have on the exam.

64. Example A part-time mover’s regular pay rate is $6 per hour. If the work involves going up and down stairs, his rate increases to $9 per hour. In one week he earned $138 and worked 20 hours. How many hours did he work at each rate?

65. Example Suppose 95 people attended a rock concert. Ticket prices were $60 for reserved seats and $40 for general seating. If 30 people bought reserved seats, how much money was received from the sale of the reserved seats and how much was received from the sale of the general seats?

66. Example In order to receive your degree, the college has decided that you must complete 90 units of college credit. Suppose you have already completed 60 units of credit. How long would it take you to satisfy the requirements if you take 10 units per semester? If you want to graduate in two semesters, how many units should you take each semester?

67. Example After receiving their tax refund, a couple split the refund equally. The husband then gave $50 of his refund to charity, leaving him with $70. What was the amount of the tax refund?

68. Example A fitness club has 150 members. Monthly membership fees are $25 for those under 65 and a special senior rate of $15 for those 65 and older. If there are twice as many seniors as regular paying customers, how much does the club receive each month?

69. Recall that exponents are used to indicate repeated multiplication.

70. Simplify the following:

71. The Product Rule for Exponents If x is any number and m and n are integers, then

72. Simplify the following:

74. The Power Rule for Exponents If x is any number and m and n are integers, then

75. Simplify the following

77. The Power Rule for Products If x and y are any numbers and m is any integer, then

78. Simplify the following:

79. Any Questions???