Dependent Voltage Source KCL question

[sdusheyko]

I'm having trouble figuring out the KCL portion of this problem.

I have no idea how in the world the solution does from;

(2-v)/20 = (Vx-2Vx)/8 - (Vx-8)/4

to;

17V - 18Vx = 84

it doesn't seem to make sense; but neither does my solution. i think I'm missing some concept here but cannot put my figure on it.

Thanks.

 

[xcvxcvvc]

By eyeballing it, I'd say the solutions manual probably multiplied the entire equation by some constant to make all the fractions go away.