Does anyone know how to do the opposite of distribution? I give medal.

- anonymous

Does anyone know how to do the opposite of distribution? I give medal.

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- anonymous

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

- Nnesha

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

- 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

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## More answers

- Nnesha

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

- Nnesha

btw there is one with x
1x-3xy

- anonymous

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

- Nnesha

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

- anonymous

1-3y=1/x

- Nnesha

perfect

- Nnesha

what would be the next step ?

- anonymous

-3y=1/x -1

- anonymous

|dw:1441832388127:dw|

- Nnesha

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

- Nnesha

so \[\frac{ \frac{ 1 }{ x } }{ -3 } = ?\]

- anonymous

0_0

- Nnesha

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

- anonymous

|dw:1441832579715:dw|

- Nnesha

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

- anonymous

|dw:1441832707298:dw|

- anonymous

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

- Nnesha

5 how did u get 5 ?

- Nnesha

what is the reciprocal of `-3/1` > ?

- 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.

- anonymous

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

- Nnesha

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

- Nnesha

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

- anonymous

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

- Nnesha

yes right substitute x for -5

- anonymous

|dw:1441833342964:dw|

- Nnesha

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

- anonymous

|dw:1441833454633:dw|

- Nnesha

hmm no

- 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

- anonymous

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

- Nnesha

just multiply the numerator by numerator and the denominator by denominator

- Nnesha

no not cross multiplication

- anonymous

ok|dw:1441833634950:dw|

- anonymous

|dw:1441833735641:dw|

- 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

- anonymous

|dw:1441833868729:dw|

- anonymous

so y = 4/15?

- Nnesha

no

- anonymous

what part was wrong in my solving?

- Nnesha

|dw:1441834075300:dw|

- Nnesha

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

- anonymous

I got -1/15

- Nnesha

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

- Nnesha

|dw:1441834239060:dw|
negative should cancels out

- anonymous

what positive number is the -1 being multiplied by?

- anonymous

-1*

- anonymous

negative* ^^

- 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

- anonymous

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

- 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 ?

- anonymous

|dw:1441834466580:dw|

- Nnesha

lO_Oks good! great job!

- 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.

- Nnesha

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

- anonymous

thank you. good bye

- Nnesha

good bye

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