Rearranging Formula: Step-by-Step Guide to Solve ax - b = cx + d

[Gringo123]

I have been trying to rearrange this formula to make x the subject:

ax - b = cx + d

My (wrong) attempt at the answer was:

x = cx + d/a - b

I know that that is wrong because x still appears on the right side of the formula. The right answer is:

x = (d+b)/(a-c)

I have no idea how to arrive at that. Can anyone talk me through it step by step?
Thanks

 

[denverdoc]

sure: first collect all the x terms on one side by subtracting cx from both sides:

ax-cx-b=d

now collect all the non x terms on the opposite side by adding b to both sides.

ax-cx=b+d now factor out x so that it looks like x(a-c). Divide both sides by what now?

 

[Gringo123]

Divide both sides by (a-c) and you get:
x = (d+b) / (a-c)
Thanks a lot Denverdoc! It was very kind of you to help out.

 

[denverdoc]

no problem; btw there is a math forum here for various issues you may run into. fine that you posted here, but in future may wish to consider it.