I'm asked to determine \$ V_x, I_x \$ in this circuit  :

First, from first look the middle "mesh" is incomplete so there is no complete path for I_x to return thus KCL requirements aren't fulfilled, so

\$ I_x = 0 A \$

Second, we can work on the two other meshes independently, \$ 8 = (4+2)i_1 \iff i_1 = 1.333 A \$ and \$ 4 = (6+3)i_2 \iff i_2 = \frac{4}{9} A \$ thus \$ V_x = - 2.667 V \$

Is this logic correct or is there a flaw?

I'm asked to determine \$ V_x, I_x \$ in this circuit:

First, from first look the middle "mesh" is incomplete so there is no complete path for I_x to return thus KCL requirements aren't fulfilled, so

\$ I_x = 0 A \$

Second, we can work on the two other meshes independently, \$ 8 = (4+2)i_1 \iff i_1 = 1.333 A \$ and \$ 4 = (6+3)i_2 \iff i_2 = \frac{4}{9} A \$ thus \$ V_x = - 2.667 V \$

Is this logic correct or is there a flaw?

Im asked to determine \$ V_x, I_x \$ in this circuit :

First, from first look the middle "mesh" is incomplete so there is no complete path for I_x to return thus KCL requirements arent fullfilled, so  \$ I_x = 0 A \$ Second, we can work on the two other meshes independently, \$ 8 = (4+2)i_1 \iff i_1 = 1.333 A \$ and \$ 4 = (6+3)i_2 \iff i_2 = \frac{4}{9} A \$ thus \$ V_x = - 2.667 V \$ is this logic correct or is there a flaw?

I'm asked to determine \$ V_x, I_x \$ in this circuit :

First, from first look the middle "mesh" is incomplete so there is no complete path for I_x to return thus KCL requirements aren't fulfilled, so 

\$ I_x = 0 A \$

Second, we can work on the two other meshes independently, \$ 8 = (4+2)i_1 \iff i_1 = 1.333 A \$ and \$ 4 = (6+3)i_2 \iff i_2 = \frac{4}{9} A \$ thus \$ V_x = - 2.667 V \$

Is this logic correct or is there a flaw?