Simple Algebra Equation I have a simple part of a question to solve.  The problem is my answer is different to the solution in my textbook.
The equation is: $$\frac{5v}{6} = \frac{(\frac{1}{2}a+b+\frac{1}{2} c)v}{a+b+c}$$
I am supposed to get $$\frac{2}{3}(a+b+c) = b$$
But I simply get: $$b=2a +2c$$
I get my answer by cross multiplying.  I then use my answer to get $\frac{b}{a+b+c}$ as some fraction.  I have not worked onto this stage as I am unsure about the above work.
What am I doing wrong here? 

What you get is equivalent to what you're supposed to get.
$ b= 2a+2c \implies 3b=2a+2c+2b \implies b= 2(a+b+c)/3$
