Verified answer

Changing Voltage Sources into current sources using Source Transformations:

http://en.wikipedia.org/wiki/Source_transformation

The 4V and 3.5 ohm becomes a 4V / 3.5 ohm = 1.1429 Amp current source (out from the right) in parallel to the 3.5 ohms.

The 1V and 2.0 ohm becomes a 1V / 2 ohm = 0.5 Amp current source (out from the left) in parallel to the 2 ohm.

The current sources subtract as 1.1429 A (right) - 0.5 A (left) = 0.6429 (out from the right)

And this current is then found into the 2 ohm using current dividers, but first combining the 3.5 ohm and 1.0 ohm in parallel yields 3.5 / 4.5 = 0.7778 ohms in parallel to the 2 ohms.

http://en.wikipedia.org/wiki/Current_divider

The current divider equation is therefore

I = 0.6429 A * (0.7778 / (0.7778 + 2) ) = 0.6429 A * 0.28 = 0.18 Amps (in from the right, out to the left)

Sorry for the confusion in the explanation, but drawing it out will help clarify.