## anonymous one year ago Does anyone know how to do the opposite of distribution? I give medal.

1. anonymous

x-3xy = 1. I have to solve for y

2. Nnesha

well for opposite of distribution you have to take out the common factor like aB+aC= a(b+c)

3. anonymous

but do I have to for this problem do a fraction because their is no Y for the x in the front of the problem. It has to be something like y(___ +3x) = 1

4. Nnesha

well what is common in these two terms x-3xy ??

5. Nnesha

btw there is one with x 1x-3xy

6. anonymous

the x is common so should I try to turn that into a distributive problem first? I would get x(1+3y)= 1

7. Nnesha

yes right but 3y is negative so $\huge\rm x(1-3y)=1$ now move the x to the right side

8. anonymous

1-3y=1/x

9. Nnesha

perfect

10. Nnesha

what would be the next step ?

11. anonymous

-3y=1/x -1

12. anonymous

|dw:1441832388127:dw|

13. Nnesha

yes right so both terms are dividing by -3 so you can write it as |dw:1441832500945:dw|

14. Nnesha

so $\frac{ \frac{ 1 }{ x } }{ -3 } = ?$

15. anonymous

0_0

16. Nnesha

o^_^o multiply the top with the reciprocal of the bottom

17. anonymous

|dw:1441832579715:dw|

18. Nnesha

|dw:1441832658208:dw| 1/x not 5 yes right now multiply the top fraction with the reciprocal of the bottom fraction

19. anonymous

|dw:1441832707298:dw|

20. anonymous

I might have forgotten how to multiply fractions. it is from left to right, right? not cross multiplication

21. Nnesha

5 how did u get 5 ?

22. Nnesha

what is the reciprocal of -3/1 > ?

23. anonymous

Oh I'm sorry I didn't put the second part of the question. x-3xy = 1. Solve for y. then find y if x = -5.

24. anonymous

the reciprocal of -3/1 is 1/-3

25. Nnesha

alright first we should solve for y then we can replace by -5 and yes reciprocal|dw:1441833141499:dw| is 1/-3

26. Nnesha

$\huge\rm y=\frac{ 1 -}{ x } \times \frac{ 1 }{ -3 }-\frac{ 1 }{ -3 }$ simplify this first then substitute x for -5

27. anonymous

So, now I got the equation for y and I need to plug in X for what y =s

28. Nnesha

yes right substitute x for -5

29. anonymous

|dw:1441833342964:dw|

30. Nnesha

$\huge\rm y=\frac{ 1 -}{ x } \times \frac{ 1 }{ -3 }-\frac{ 1 }{ -3 }$ first simplify this

31. anonymous

|dw:1441833454633:dw|

32. Nnesha

hmm no

33. Nnesha

$\huge\rm y=\color{ReD}{\frac{ 1 -}{ x } \times \frac{ 1 }{ -3 }}-\frac{ 1 }{ -3 }$ simplify the red part first don't replace x for -5 yet

34. anonymous

i do this by cross multiplication? or does the answer of the numerator have to be the same as the denominator?

35. Nnesha

just multiply the numerator by numerator and the denominator by denominator

36. Nnesha

no not cross multiplication

37. anonymous

ok|dw:1441833634950:dw|

38. anonymous

|dw:1441833735641:dw|

39. Nnesha

yes right so negative divide by negative equal positive so -1/-3 $\huge\rm y = -\frac{ 1 }{ 3x }+\frac{ 1 }{3 }$ and there is typo it should be 1/-3x sorry about that

40. anonymous

|dw:1441833868729:dw|

41. anonymous

so y = 4/15?

42. Nnesha

no

43. anonymous

what part was wrong in my solving?

44. Nnesha

|dw:1441834075300:dw|

45. Nnesha

|dw:1441834145872:dw| negative divide by negative = positive

46. anonymous

I got -1/15

47. Nnesha

that was your mistake ^^^^ negative divide by negative = posistive

48. Nnesha

|dw:1441834239060:dw| negative should cancels out

49. anonymous

what positive number is the -1 being multiplied by?

50. anonymous

-1*

51. anonymous

negative* ^^

52. Nnesha

|dw:1441834316056:dw| 3 times -5 = -15 so both negatives ( numerator and the denominator one would cancel each other out) that was your mistake other works is right so now add instead subtraction

53. anonymous

ok that's what i didn't understand how they numerator and the denominator both get their sign changed

54. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @Nnesha yes right so negative divide by negative equal positive so -1/-3 $\huge\rm y = -\frac{ 1 }{ 3x }+\frac{ 1 }{3 }$ and there is typo it should be 1/-3x sorry about that $$\color{blue}{\text{End of Quote}}$$ this is what we got after solving for y agree ?

55. anonymous

|dw:1441834466580:dw|

56. Nnesha

lO_Oks good! great job!

57. anonymous

Thank you so much I have a big Alg 2 test tomorrow. And what i learned from you about fractions saved my life. :D Sorry it took so long.

58. Nnesha

it was fun working with you great student! i wish you all the best for the test good luck!!!! focus on signs !!!

59. anonymous

thank you. good bye

60. Nnesha

good bye