## anonymous one year ago ...

1. anonymous

The answer sheet says the odd integers are 15, 17, and 19. I have no idea whats going on

2. tkhunny

You must NAME the three integers. Do that first.

3. anonymous

x = first odd integer?

4. tkhunny

Good try, but it is only by luck that it will be odd. How do you REQUIRE it to be odd?

5. anonymous

well

6. anonymous

You don't have to go to that extent. Because they are consecutive odd integers, you know exactly what the difference is between the third one and the first one. Then the question becomes much simpler.

7. anonymous

ohh yeah thats true

8. tkhunny

That may be true for this problem, but it is not a general solution to all such problems. Name the three odd integers.

9. anonymous

Let the second odd integer be \(x\) and build a fairly simple equation based on the question.

10. anonymous

A general solution is not required for a specific problem.

11. anonymous

okay im gonna try and figure it out right now

12. tkhunny

A general solution is required for ALL problems. We can worry about esoterica later. If you are in a contest, where speed is of the essence, let's find all the speed-up, short cuts we can. When we are learning to be consistent, correct, and easily followed, please be more deliberate and distinct. Name the three integers.

13. anonymous

would the third integer be 4?

14. tkhunny

Does that sound odd to you? What did you name the integers?

15. anonymous

no it doesnt

16. anonymous

How much is 3 times the difference between the 3rd and 1st odd integer?

17. sohailiftikhar

ok first know that the sum and difference of two odd integers is even

18. tkhunny

Ah! Another single-problem solver.

19. sohailiftikhar

now consider three consecutive odd integers 2x+1, 2x+3,2x+5

20. anonymous

hmm

21. sohailiftikhar

now can you solve it ?

22. anonymous

yeah i can but how did you get it? Three times the difference of the third and first odd integer is five less than the second odd integer so do you have to multiply or subtract?

23. sohailiftikhar

what is that mean ?'' single-problem solver ''

24. tkhunny

Seriously, if you effectively name the integers, everything everyone is trying to tell you will be seen clearly before your eyes. To bad soha... did the naming for you. It would have been useful to have you come up with that. Keep in mind that it is not the only definition. It could be 2x-1, 2x+1, 2x+3. You just have to keep track of your clear and useful definitions. You were originally going for x,x+2,and x+4. That MIGHT work, but only if you get luck and find a solution where x is odd. With 2x+1, knowing that x is an integer, 2x+1 MUST be odd.

25. sohailiftikhar

yes you can also consider these numbers as well

26. anonymous

yeah.. uh

27. sohailiftikhar

2x+1 is odd

28. tkhunny

1st odd integer: 2x+1 2nd odd integer: 2x+3 3rd oddineger: 2x+5 Build it from the problem statement.

29. sohailiftikhar

yes

30. anonymous

yeah i can do that.. but like im so lost on how you guys found the integers

31. tkhunny

We didn't FIND them. We just NAMED them.

32. anonymous

oh okay

33. sohailiftikhar

here first know this thing that odd integers are 1,3,5,7..... now these are like 2x+1 here put any value of x you will get odd integer try it

34. anonymous

okay got it :)

35. tkhunny

If you KNOW x is an integer, then 2x is an EVEN integer and 2x+1 is an ODD integer. That's all.

36. sohailiftikhar

know you have to consider three consecutive odd integers so you can consider 2x+1,2x+3,2x+5 or 2x-1,2x+1,2x+3

37. triciaal

another approach

38. triciaal

|dw:1441085018113:dw|

39. triciaal

|dw:1441085108455:dw|

40. sohailiftikhar

no you can consider these numbers because you don't know what x is

41. sohailiftikhar

you are using answers to make integers huh ...? lol

42. tkhunny

No,see, triciaal is using the magic method. It will only be by luck if x turns out to be odd.

43. triciaal

x is an odd integer to count by odd numbers you are counting by 2's

44. anonymous

yeah starting to understand now lol

45. tkhunny

You can SAY it is odd, but if your solution produces x = 14 what will you do?

46. sohailiftikhar

but we are discussion the general method right ? so we have to use proper way

47. anonymous

yeah its general strategy

48. anonymous

but idk

49. triciaal

@tkhunny what magic method? go back to basics count by 2's for the next number

50. tkhunny

Asked and answered. You do not KNOW that x will be odd. You have defined ODD or EVEN consecutive integers. There is nothing in your definition that REQUIRES them to be odd.

51. sohailiftikhar

ok so we done now ?

52. triciaal

the question said it was odd

53. sohailiftikhar

agree with @tkhunny

54. tkhunny

55. anonymous

Thank you guys for your help, I will eventually figure it out. :)

56. sohailiftikhar

we ca solve questions of math by different methods but we have to use a proper method to solve a general problem

57. sohailiftikhar

np :)

58. triciaal

@glitterythings do you want me to review what I did ?

59. tkhunny

...and I retract my statement where I called @sohailiftikhar a single-problem solver.

60. anonymous

if you dont mind

61. anonymous

@triciaal

62. sohailiftikhar

@tkhunny :)

63. triciaal

x is an odd integer consecutive means in counting order to count by odd numbers example 1, 3, 5 7 counting by 2's so before x will be (x-2) and after x will be (x +2)

64. triciaal

next use the information given to set up the equation

65. anonymous

Can i always use that method? but with different information?

66. tkhunny

{sigh} And if you are lucky, x will turn out to be odd. You can always solve with a method that REQUIRES your result to take on the REQUIRED form.

67. triciaal

|dw:1441085808490:dw|

68. triciaal

simplify the equation, solve for x

69. triciaal

is it clear now?

70. anonymous

yeah it is

71. triciaal

great

72. anonymous

thx!