Solve for y!

Question

The equation is:

w = (3y-x)/y

And I have to solve for y. How do I do this?

Answer 1

To "solve" for y means to change the equation to look like this:    y = ...

    That will provide value(s) of y that make the equation true.

 

First of all, note that y≠0 since division by 0 is not defined (remember this later).

 

In order to do that, break the current expressions down and perform the opposite operations:

     for +, do -

     for -, do +

     for *, do /

     for /, do *

 

Given:

    w = (3y-x)/y

    w = (3y - x)(1/y)                    [re-write]

    w = (3y)(1/y) - (x)(1/y)           [distribute]

    w  = 3  - x/y                           [y cancels]

    w - 3 = -x/y                          [subtract 3 from both sides]

   y(w-3) = -x                            [multiply both sides by y]

    y = -x/(w-3)    with (y≠0 and w≠3)         [divide both sides by (w-3)]

        Note:  this could also be written as:

                 y = x/(3-w)    with (y≠0 and w≠3)