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

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

Mathematics
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x-3xy = 1. I have to solve for y
well for `opposite of distribution` you have to take out the common factor like aB+aC= a(b+c)
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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well what is common in these two terms x-3xy ??
btw there is one with x 1x-3xy
the x is common so should I try to turn that into a distributive problem first? I would get x(1+3y)= 1
yes right but 3y is negative so \[\huge\rm x(1-3y)=1\] now move the x to the right side
1-3y=1/x
perfect
what would be the next step ?
-3y=1/x -1
|dw:1441832388127:dw|
yes right so both terms are dividing by -3 so you can write it as |dw:1441832500945:dw|
so \[\frac{ \frac{ 1 }{ x } }{ -3 } = ?\]
0_0
o^_^o multiply the top with the `reciprocal` of the bottom
|dw:1441832579715:dw|
|dw:1441832658208:dw| 1/x not 5 yes right now multiply the top fraction with the reciprocal of the bottom fraction
|dw:1441832707298:dw|
I might have forgotten how to multiply fractions. it is from left to right, right? not cross multiplication
5 how did u get 5 ?
what is the reciprocal of `-3/1` > ?
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.
the reciprocal of -3/1 is 1/-3
alright first we should solve for y then we can replace by -5 and yes reciprocal|dw:1441833141499:dw| is 1/-3
\[\huge\rm y=\frac{ 1 -}{ x } \times \frac{ 1 }{ -3 }-\frac{ 1 }{ -3 }\] simplify this first then substitute x for -5
So, now I got the equation for y and I need to plug in X for what y =s
yes right substitute x for -5
|dw:1441833342964:dw|
\[\huge\rm y=\frac{ 1 -}{ x } \times \frac{ 1 }{ -3 }-\frac{ 1 }{ -3 }\] first simplify this
|dw:1441833454633:dw|
hmm no
\[\huge\rm y=\color{ReD}{\frac{ 1 -}{ x } \times \frac{ 1 }{ -3 }}-\frac{ 1 }{ -3 }\] simplify the red part first don't replace x for -5 yet
i do this by cross multiplication? or does the answer of the numerator have to be the same as the denominator?
just multiply the numerator by numerator and the denominator by denominator
no not cross multiplication
ok|dw:1441833634950:dw|
|dw:1441833735641:dw|
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
|dw:1441833868729:dw|
so y = 4/15?
no
what part was wrong in my solving?
|dw:1441834075300:dw|
|dw:1441834145872:dw| negative divide by negative = positive
I got -1/15
that was your mistake ^^^^ negative divide by negative = posistive
|dw:1441834239060:dw| negative should cancels out
what positive number is the -1 being multiplied by?
-1*
negative* ^^
|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
ok that's what i didn't understand how they numerator and the denominator both get their sign changed
\(\color{blue}{\text{Originally Posted by}}\) @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 ?
|dw:1441834466580:dw|
lO_Oks good! great job!
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.
it was fun working with you great student! i wish you all the best for the test good luck!!!! focus on signs !!!
thank you. good bye
good bye

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