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I have a formula $y-ya-x=0$ where y can be isolated to $y=-\frac{x}{a-1}$ (Thanks to wolframalpha). It have been a few years since i have been doing math, but i would like to know what the steps are in isolating y in this formula?

The formula is used to calculate the sale price of a house to break even, where x is the purchase price, y is the sales prices and a is the percentage agents take of the sales price y to sell the house.

Example: I bought a house for 300k, and it costs 6% to sell the house. $y-y0.06-300000=0$ where y is $y=-\frac{300000}{0.6-1}=319148.93617$, we need to sell the house for 320k to break even on the sale.

clathratus
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Androme
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  • Please format your questions using MathJax. This page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. – Brian61354270 Mar 12 '19 at 01:19

1 Answers1

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the steps are simply, if you want to isolate $y$ on $y-ya-x=0$ you can proced as folowing:

$$y-ya-x=0\\ y-ya-x+x=0+x\\ y-ya=x\\ y(1-a)=x\\ y(1-a)\div(1-a)=x\div(1-a)\\ y=\frac{x}{1-a}\\ y=\frac{x}{-1(a-1)}\\ y=-\frac{x}{a-1}$$

the ideia where is that if you have a equation, additing or subtracting a value won't break the equality as long you do in both side so:

in step 2 you sum $x$ in either side to isolate $y$ on a side of equation.

on step 3 to 4 we did a factoration, since y was in both terms you can write it only 1 time it, then you divide all the terms by that value and pit then inside the parents, like $y-ya=y(1-a)$

on step 5 worked like what was explained on step 2, multiplyng or dividing both side by same value won't break the equation (as long you be carefull of not dividing by 0)

the finals step just use the fact that $1-a=-(a-1)$, you can see that like you factoring $-1$ there.

does this help you understand it better?

cand
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