I need to make x the subject of the following formula. 2y = (5 - square root of x)/ 3
I am assuming that you would like to solve the equation for x.
2y = (5- sqrt x) /3
You want to isolate x. In order to do that, you first must multiply both sides of the equation by 3.
3 * 2y = [(5 - sqrt x)/3] *3
6y = 5 - sqrt x
Now you need to isolate the square root part. To do this, you need to subtract the 5 from both sides.
6y - 5 = 5 - sqrt x - 5
6y - 5 = -sqrt x
That negative sign is messing things up, so get rid of it next. Simply multiply both sides by -1. (Change ALL of your signs.)
Your result: 5 - 6y = sqrt x
All this while, you have been doing the opposite of what is there. The same thing needs to be done to get rid of the sqrt. Square both sides of your equation.
(5 - 6y)^2 = (sqrt x)^2
(5 - 6y)^2 = x
Now you can either leave it like that, or you can go ahead and square that binomial out on the left side, using FOIL. If you want to go ahead and square it, you will get:
25 - 60y + 36y^2 = x
Rearrange to put it in standard form:
36y^2 - 60y + 25= x.
So, your answer can be either
(5 - 6y)^2 = x
36y^2 - 60y + 25 = x
Here y is expressed through x. Saying x through y is to find inverse the function.
To find x through y (and making x the subject)we follow like this:
Multiply both sided by 3 to get rid of the dinominator.
Subtract 5 from bothsides:
Square both sides:
x=(6y-5)^2 . This is a statement or sentence which is read like:
x is equal to six y minus 5 whole square.
In the above sentence x is the subject( and the rest is predicate.)