1. Unit 4a You will be required to show your work even it you can do it in you head!!

2. Question 1 Is 25 the solution for 3x +6 = 81?

3. Explanation for # 1 Substitute the number given for the variable in the equation and use the order of operations to see if the equation is balanced!! Is 25 the solution for 3x +6 = 81? 3. 25 + 6 = 81 75 + 6 = 81 81 + 81 So, yes, 25 is the solution!!

4. Question 2 Is 104 the solution for x - 4 = 99?

5. Explanation for #2 Substitute the number given for the variable in the equation and use the order of operations to see if the equation is balanced!! Is 104 the solution for x - 4 = 99? 104 – 4 = 99 100 = 99 100 does NOT equal 99 so 104 is NOT the solution!!

6. Your Turn Is 24 the solution for 3x + 3 = 75? Is 75 the solution for x – 15 = 65? 3x + 3 = 75 3. 24 + 3 = 75 72 + 3 = 75 75 = 75 YES!!! x – 15 = 65 75-15 = 65 60 = 65 NO!!!

7. Homework Is 15 the solution for 3x + 3 = 48? Is 100 the solution for x – 15 = 85?

8. Question 3 Which equation has x = 3 as the solution? 2 + x = 7 3x = 9 2x = 18 x + 3 = 9

9. Question 4 Which equation has x = 9 as the solution? 2 + x = 7 3x = 9 2x = 18 x + 3 = 9

10. Explanation for # 3 & #4 Which equation has x = 3 as the solution? 2 + x = 7 3x = 9 2x = 18 x + 3 = 9 Substitute 3 for x in each equation to see which one is true!! EASY 2 + 3 = 7 NOPE 3. 3 = 9 YES 2. 3 = 18 NOPE 3 + 3 = 9 NOPE Which equation has x = 9 as the solution? 2 + x = 7 3x = 9 2x = 18 x + 3 = 9 Substitute 9 for x in each equation to see which one is true!! EASY 2 + 9 = 7 NOPE 3. 9 = 9 NOPE 2. 9 = 18 YES 9 + 3 = 9 NOPE

11. Your Turn Which equation has x = 5 as the solution? 3 + x = 12 3x = 15 2x = 18 x + 3 = 9 3 + 5 = 12 NOPE 3. 5 = 15 YES!! 2. 5 = 18 NOPE 5 + 3 = 9 NOPE

12. Homework Which equation has x = 12 as the solution? 2 + x = 10 2x = 18 x + 3 = 15 3x = 21 Which equation has x = 7 as the solution? 2 + x = 10 2x = 18 x + 3 = 9 3x = 21

13. Question 5 Solve 16 = z-3

14. Question 6 Solve n + 12 = 19

15. Question 7 Solve s + 5.3 = 11

16. Explanation for #7 & 10 s + 5.3 = 11 s + 5.3-5.3 = 11-5.3 s = 5.7 Don’t forget to line up the decimals when you add or subtract!! 11.0 - 5.3

17. Question 8 Solve 6w = 4.2

18. Explanation for # 8 6w = 4.2 6 6 6 4.2 w = 0.7 0. 7 Don’t forget that when you divide decimals, the decimal goes straight up on the house!!

19. Question 9 Solve 2.5x = 8.25

20. Explanation for # 9 & 12 You need to remember how to divide decimals for both of these… 2.5x = 8.25 x = 3.3 2.5 2.5 Remember to move the decimal of the divisor to the right until you have a whole number… 2.5 8.25 becomes 25 82.5 Then just divide normally, and bring the decimal straight up!!!

21. Question 10 Solve 11.6 = x + 9

22. Question 11 Solve 12 = x + 8

23. Question 12 Solve: 23.37 = 4.1x

24. Question 13 Solve 14 = c - 88

25. Question 14 Solve x = 40

26. Explanation for # 14 Solve x = 40 Use the inverse operation of division to solve this.  x = 40  Now, all you have to remember is “Keep it, change it flip it” to solve!! x = 80

27. Your Turn 21 = z-5 x = 30 18 = c – 95 21.42 = 1.4x z = 26 x = 60 c = 113 x = 15.3

28. Homework 31 = z-7 x = 32 28 = c – 64 4.5 = 1.8x

29. Question 15 Mary paid $25 for 5 cans of hair spray. If x represents the cost of can of hair spray, which equation could be used to find the cost of ONE can of hair spray? 25x = 5 x + 5 = 25 25 + 5 = x 5x = 25

30. Explanation for # 15  Here is Mary….  Here is the hair spray….  Here is the money…. What do we know about the hairspray? She bought 5 cans! What do we know about the money? She spent $25! What equation can we write? We know she bought 5 cans. We know she spent $25. We know that x = 1 can.

31. Your Turn Dr. Brantley paid $16 for 4 packages of jelly beans. If x represents the cost of 1 package of jelly beans, which equation could be used to find the cost of ONE package of jelly beans?

32. Homework Dr. Brantley paid $12 for 4 packages of pens. If x represents the cost of 1 package of pens, which equation could be used to find the cost of ONE package of pens?

33. Question 16 Bailey is 5 years younger than her sister Shelby. If Bailey is 13, which equation represents Shelby’s age? s – 5 = 13 s + 5 = 13 13 - s = 5 s + 13 = 5

34. Explanation for #16 Here is Shelby. What do we know about Bailey? She is 5 years younger (LESS) than Shelby. She is 13. Here is Bailey. What do we know about Shelby? She is older than Bailey. Her age is s. What equation can we write to figure out how old Shelby is?

35. Your Turn Mary is 16 years younger than her sister Jessica. Let j = Jessica’s age. If Mary is 12, write 4 equations that represent Jessica’s age.

36. Homework Mary is 14 years younger than her brother, Joey. Let j = Joey’s age. If Mary is 12, write 4 equations that could be used to determine Joey’s age.

37. Question 17 Dr. Brantley put $50 worth of gas in her car. If the price per gallon was $3.50, which equation could be used to figure out how many gallons she put in her car? 3.50g = 50 50g = 3.50 50 = 3.50 + g 50 + g = 3.50

38. Explanation for # 17 Here is Dr. Brantley’s car : Gas is $3.50 a gallon. Dr. Brantley spent $50. g = 1 gallon of gas Remember if we know what one is ($3.50), then we can figure out what more than one is by… MULTIPLYING!!!

39. Your Turn Dr. Brantley put $30 worth of gas in her car. If the price per gallon was $2.50 which equation could be used to determine how many gallons she put in her car? 2.50g = 30 2.50 + g = 30 30g = 2.50 30 + g = 2.50 Remember if we know what one is, then we can figure out what more than one is by performing which operation? + - x 

40. Homework Dr. Brantley put $40 worth of gas in her car. If the price per gallon was $2.65 which equation could be used to determine how many gallons she put in her car? 40g = 2.65 40 + g = 2.65 2.65 + g = 40 2.65g = 40 Remember if we know what one is, then we can figure out what more than one is by performing which operation? + - x 

41. Question 18 The area of the floor in Chan’s room is 48.6 square meters. If the width of his room is 5.4 meters, what is the length of his bedroom? (Area = length x width)

42. Explanation for #18 This is a matter of plugging in what you know and solving a one- step equation for what you don’t!!! We know that (Area = l ength x width) We know the area of Chan’s room: We know the width of his room: Now, plug those numbers into the equation and solve! 48.6 square meters 5.4 meters 48.6 = l. 5.4

43. Your Turn The area of the floor in your room is 64.8 square meters. If the width of yours room is 5.4 meters, what is the length of your bedroom? (Area = length x width) 64.8 = l. 5.4 5.4 5.4 12 =

44. Homework The area of the floor in your room is 57.6 square meters. If the width of yours room is 7.2 meters, what is the length of your bedroom? (Area = length x width)

45. Question 19 Dr. Brantley bought $15 more in groceries this week than she did last week. If she spent $25 this week, choose the equation that will determine the amount she spent last week. 15x = 25 15 + x = 25 25 + x = 15 25x = 15

46. Explanation for # 19 Here are this week’s groceries What do we know? I spent $25 this week. That is $15 more this week than last week! UGH!! Here are last week’s groceries What do we know? I spent $15 less on these groceries. x = last week’s groceries What are the terms in the equation? 1525x How could we arrange these terms? $25 x

47. Your Turn Dr. Brantley bought $12 more in groceries this week than she did last week. If she spent $36 this week, choose the equation that will determine the amount she spent last week. 12x = 36 36 + x = 12 36x = 12 12 + x = 36 The terms of the equation are 12, 36 and x. I can represent this situation several different ways: 36- 12 = x 36 - x = 12 12 + x = 36 x + 12 = 36

48. Homework Dr. Brantley bought $18 more in groceries this week than she did last week. If she spent $48 this week, choose the equation that will determine the amount she spent last week. 48 + x = 18 48x = 18 18x = 48 18 + x = 48

49. Question 20 The sum of a number and 15 is 47. Write an equation and solve. Explain how you would solve, using the magic phrase, “inverse operation”.

50. Explanation for #20 The sum of a number and 15 is 47. Write an equation and solve. Explain how you would solve, using the magic phrase, “inverse operation”. Since the “sum” is the answer to an addition problem, I know I need to add. I know the sum is 47, so I give the unknown a variable, n. My equation is: 15 + n = 47 I use the inverse of addition, which is subtraction, to isolate the variable: 15-15 + n = 47–15. You have to do same operation on both sides of the equation to keep it balanced. So, n = 32.

51. Your Turn The sum of a number and 15 is 32. Write an equation and solve. Explain how you would solve, using the magic phrase, “inverse operation”. Since the “sum” is the answer to an addition problem, I know I need to add. I know the sum is 32, so I give the unknown a variable, n. My equation is: 15 + n = 32. I use the inverse of addition, which is subtraction, to isolate the variable: 15-15 + n = 32–15. You have to do same operation on both sides of the equation to keep it balanced. So, n = 17.

52. Homework The sum of a number and 22 is 63. Write an equation and solve. Explain how you would solve, using the magic phrase, “inverse operation”.

53. Question 21 Steve had $10 in his wallet. He purchased a bottle of water for $1.50 and he bought a magazine. When he left the store, the cashier gave him $5.25 in change. Determine the cost of the magazine.

54. Explanation for #21 Here is Steve and his $10.00 Here is the bottle of water. Here is the magazine. Her is the change. What do we know? Water costs $1.50. His change was $5.25. Steve paid with a $10 bill. He starts with 10.00. He spends 1.50 and m and gets 5.25 in change. What operation do we need?????

55. Your Turn Ms. Andrews had $20 in her wallet. She bought some marshmallows for $2.25 and a candy bar. When she left the store, the cashier gave him $12.65 in change. Determine the cost of candy bar. 20 = 2.25 + 12.65 + m 20-2.25-12.65 = 2.25-2.25+ 12.65-12.65 + m 17.75 – 12.65 = m 5.10 = m

56. Homework Ms. Landing had $15 in her wallet. She bought some crayons for Alaina for $3.25 and a new binder. When she left the store, the cashier gave her $4.55 in change. Determine the cost of the binder.