1. ## Isolating a value

Hi, maths is a long time ago for me and I need to solve this equation (if its possible). I've read where to post but its been so long I'm still not sure so if this isnt the right area then I apologise.

I have a formula where,

x = a - b + (((a+b)/2) * e) * f

is it possible to rearrange this formula so I could isolate b i.e. b = ?

Any help would be greatly appreciated
Many thanks
Steve

2. I believe you can:

$\displaystyle x = a - b + ef\,\dfrac{a+b}{2}\quad\to$

$\displaystyle x-a=-b+ef\,\dfrac{a+b}{2}=-b+\dfrac{efa}{2}+\dfrac{efb}{2}\quad\to$

Can you continue?

3. Thank you Adrian, very much appreciated.

I've tried to complete it from here but I'm getting stuck. It's for a work assignment which i hope can be solved this way but I just wish I continued with Maths at school. I'm getting stuck removing the division to isolate the b? am I on completely the wrong track?

Thanks again
Steve

4. Well, can you show me what you've done?

5. by all means but please be kind this is my first attempt at trying to remember how to do this. I've just ordered some books from Amazon.

x - a - efa/2 = -b + efb/2

x- a - efa/2 = -b + b(ef/2)

from there I feel I want to square both sides to get rid of the divide but then I just get lost?

6. Great so far! I wouldn't square both sides. Instead, I would factor the b out of both terms on the RHS.

7. would that make the RHS -b(1-ef/2)? is that allowed?

I am enjoying this, breaking out of the norm

8. is this correct?

- ( x - a) - efa/2 = b
1 - ef/2

if the format is off I'll repost, if this is correct is this the neatest solution?
Thanks again

9. You're close, but I think your factorization of -b instead of b got you into sign trouble. I do this:

$\displaystyle x- a - efa/2 = -b + b(ef/2)$

$\displaystyle x- a - efa/2 = b(ef/2-1)$

$\displaystyle b=\dfrac{x-a-efa/2}{ef/2-1}.$

But you definitely have the right idea.

10. Fantastic, many many thanks Adrian, you're a lifesaver.
Kind regards
Steve

11. You're welcome. Have a good one!