Determining the voltage labeled Vx by Nodal Analysis [Voltage Controlled Current Source]
Since it is voltage controlled current source, the current from node 0 to 2 is 0.1Vx. Here replace Vx = V2-V3. So the last equation is :

$$ (V_2-V_1)/2 + (V_2-V_3)/4 - 0.1V_x =0 $$
$$ =&gt;(V_2-V_1)/2 + (V_2-V_3)/4 - 0.1(V_2-V_3)=0 $$

Solving this equation, you would get V2, since V1=50V &amp; V3 =100V