when changing the subject in an equation what should you do first?

Question

eg: y = 4a(x^2+b) over 3
multiply by 3 - 'why is this 1st'?
divide by 4a - 'why divide? how do you know to divide'?
many thanks

Answer 1

If you were to evaluate the expression on the right, you would do it in PEMDAS order (parentheses, exponents, multiply/divide, add/subtract).

In order you would evaluate the stuff in parentheses:
x² + b --> x squared first, then add b.

Then you would multiply this by 4a.

Finally you would divide this by 3.

To solve for y, you essentially do everything in reverse.

Since you divided by 3, you reverse this by *multiplying* both sides by 3.

Next to reverse the multiplication by 4a, you *divide* by 4a.

To undo the addition of b, you would subtract b.

Finally, to undo the squaring you would take the square root of both sides. (When you do this step, be sure to note that you have two roots, + and -.)

y = 4a(x² + b) / 3
3y = 4a(x² + b)
3y / 4a = x² + b
(3y / 4a) - b = x²

x = ±sqrt( 3y / 4a - b )

Does that make sense?

Answer 2

You're actually doing the opposite of "order of operations", so that you can "unwrap" the variable. In your given example, you have to multiply by 3 first, because everything else is divided by 3. You have undo the most recent operation.

:)