Can someone help me find the inverse of this equation?

Question

Y=(2x+5)/(3x-6) 

How would I check it?

Answer 1

The equation you start with

 

y=(2x+5)/(3x-6)

 

has y in terms of x. The inverse has x in terms of y. Let's go for that. Multiply both sides by 3x-6:

 

(3x-6)y = 2x + 5

3xy - 6y = 2x + 5

 

Let's get all the terms in x on one side and everything else on the other.

 

3xy - 2x = 6y + 5

x (3y-2) = 6y+5

 

So the inverse is x = (6y+5)/(3y-2).

 

Want to check it? Pop an x in the original equation and pull out a y. Then pop that y into the inverse equation and see if you get the same x. Cheers!