Need guidance with rearranging a formula with two brackets and a letter that appears.

• Feb 16th 2013, 02:14 AM
MattA147
Need guidance with rearranging a formula with two brackets and a letter that appears.
Hi guys. :) Basically as the title says can someone guide me through the problem of...

Make x the subject of

5(x-3) = y(4-3x)

Thanks any help and guidance would be greatly appreciated. :)
• Feb 16th 2013, 02:33 AM
Paze
Re: Need guidance with rearranging a formula with two brackets and a letter that appe
Hi MattA147.

The question being begged is: 'How do you solve this problem explicitly for x'.

Changing the subject of a formula basically means that if you have a formula in the form: $\displaystyle y=x+3$ then the 'subject' of the formula is 'y'. Changing the subject to 'x' would yield: $\displaystyle x=y-3$.

So in your problem we have: $\displaystyle 5(x-3)=y(4-3x)$ and we want to make 'x' the subject of the formula.

Let's start by getting rid of those parentheses:

$\displaystyle 5(x-3)=y(4-3x)\\ \Rightarrow\\5x-15=4y-3yx$

Now let's solve for 'x':

$\displaystyle 5x-15=4y-3yx\\ \Rightarrow\\5x+3yx=15+4y\\ \Rightarrow\\x(5+3y)=15+4y\\ \Rightarrow\\x=\frac{4y+15}{3y+5}$