1. ## REARRANGING EQUATIONS

rearrange these to make x the subject

V W
3X = Y

VX-W=2

6X(SQUARED) + VX = Y

2. Originally Posted by Dajaro7
rearrange these to make x the subject

V W
3X = Y

VX-W=2

6X(SQUARED) + VX = Y
1) Have you written: $\displaystyle \frac{VW}{3X}=Y$?

If so, multiply both sides of the equation by 3X.

$\displaystyle VW=3XY$

Divide both sides by 3Y.

$\displaystyle \frac{VW}{3Y}=X$

$\displaystyle \boxed{X=\frac{VW}{3Y}}$

2)

$\displaystyle VX-W=2$

$\displaystyle VX-W+W=2+W$

Divide both sides by V.

$\displaystyle \boxed{X=\frac{2+W}{V}}$

3)

$\displaystyle 6X^2+VX=Y$

Somehow, after looking at the first two, this one seems a bit out of place. I won't explain each step. I'll just perform them.

$\displaystyle 6\left(X^2+\frac{V}{6}X+\frac{V^2}{144}\right)=Y+6 \left(\frac{V^2}{144}\right)$

$\displaystyle 6\left(X+\frac{V}{12}\right)^2=Y+\frac{V^2}{24}$

$\displaystyle 6\left(X+\frac{V}{12}\right)^2=\frac{24Y+V^2}{24}$

$\displaystyle \left(X+\frac{V}{12}\right)^2=\frac{24Y+V^2}{144}$

$\displaystyle X+\frac{V}{12}=\frac{\pm \sqrt{24Y+V^2}}{12}$

$\displaystyle \boxed{X=\frac{\pm \sqrt{24Y+V^2}-V}{12}}$

I don't know how clean that last one is. Maybe some others will critique it.