Yet Another Inverse Function Problem

[beccaw]

Hi All,
So I know I just asked about an inverse function earlier today, but I came across this one and I must admit, I am stumped. The original problem is y=(9x)/(4x-7) I already switched the x's and y's to get x=(9y)/(4y-7), and then I multiplied both sides by the denominator, which gave me x(4y-7)=9y, and then divided both sides by 9 to get (4xy-7x)/9=y, but I'm lost now. Did I do all my steps correctly? How do I get the y's to all be on the same side? How do I solve for y?

 

[tkhunny]

You seem to have forgotten the concept of isolation.

x(4y-7)=9y

'y' appears on both sides. You must fix this.

4xy - 7x = 8y

4xy - 8y = 7x

Now what?

 

[beccaw]

So to get the y's on the same side, it's as simple as addition and subtraction? I was trying to think of waaaaay more confusing ways. So if I did this:

4xy-7x=9y and then subtracted and added to get:

4xy-9y=7x could I the just factor to:

y(4x-9)=7x and then just divide both sides by 4x-9?

That would give me:
y=7x/(4x-9)

 

[mmm4444bot]

and then I multiplied both sides by the denominator, which gave me x(4y-7)=9y

At this point, note that the symbol for which you're trying to solve appears inside parentheses (as well as on both sides of the equation). This situation is always a sign that the next step should be to multiply everything out and combine like terms because we can't solve for y while it appears inside grouping symbols.

That would give [the inverse relationship as]:

y=7x/(4x-9)

You are correct!



PS: When showing your work, you do not need to describe your steps in English. Simply type the equations line-by-line. We can see when you've divided both sides by something or added terms to both sides without the English descriptions. This will save you a lot of typing.