Simplifying an equation with a "looping" second equation

[Feartheblue]

I want to simplify an equation for x, where

x = c*(a+b)/2

b is never known and = a + d - x

a, c and d can be found out, so I want x to be in terms of them.

I can get to
x = c*(2a+d-x)/2, but then if I substitute for x with the first equation above, I fall into a "loop".

I know the answer is
x = c*(2a+d)/(2+c)

but I don't know how to get there. Thanks!

 

[mmm4444bot]

x = c*(a+b)/2

b is never known and = a + d - x

a, c and d can be found out, so I want x to be in terms of them.

I can get to
x = c*(2a+d-x)/2, but then if I substitute for x with the first equation above, I fall into a "loop".

Instead of substituting, try distributing the c, and then move the x-term to the left side. Next, factor and divide.

I would start by multiplying each side by 2.

2x = c(2a + d - x)

Expand the right side, using the distribution property.

2x = 2ac + cd - cx

Now get all x-terms on the left side of the equation. Then, you can factor out the x, and continue. :cool:

 

[Feartheblue]

Thanks! Looks so obvious now. I just had it in my head to substitute and couldn't look past it.