# Thread: Rearrange for "a" which appears twice

1. ## Rearrange for "a" which appears twice. Still need help!

Still Need Help

I need to rearrange this eq, for "a" however i am confused as it appears twice but understand it can be done.

X= [(a-b)/c-(a-Δ)] * [d/e]

Thanks

2. Originally Posted by chemei
I need to rearrange this eq, for "a" however i am confused as it appears twice but understand it can be done.

X= [(a-b)/c-(a-Δ)] * [d/e]

Thanks
Which is correct?

$\displaystyle X = [\frac{(a-b)}{c} - (a-\Delta)] \times \frac{d}{e}$

OR

$\displaystyle X = \frac{a-b}{c-(a-\Delta)} \times \frac{d}{e}$

Either way the first step is to divide both sides by d/e (which is the same as multiplying by e/d)

3. The second one

4. with a-b in brackets i.e (a-b)

5. Originally Posted by chemei
The second one
$\displaystyle X = \frac{a-b}{c-(a-\Delta)} \times \frac{d}{e}$

$\displaystyle \frac{a-b}{c-a+\Delta} = \frac{e}{d}X$

$\displaystyle a-b = (c-a+\Delta) \times \frac{e}{d}X = \frac{ceX}{d} - \frac{aeX}{d} + \frac{\Delta eX}{d}$

$\displaystyle a + \frac{aeX}{d} = \frac{ceX}{d} + \frac{\Delta eX}{d} + b$

Factor out a on the LHS and solve

6. Thanks for that,
I know i am asking alot but do you think you could solve for the following values, it is a long time since I have done this and am not confidient in my efforts

a=?
b=14.3
c= -18.8
d=50.6
e=18
Delta=4.6
X=1