How Accurate are My Loop Analysis Equations and Calculated Voltage?

[ee_ess_ee-kid]

Homework Statement

http://i.imgur.com/pVIMw.png

Homework Equations

KVL

The Attempt at a Solution

I called the top left loop i₁, the top right loop i₂, the bottom right loop i₃, and the bottom left loop i₄. I have all of these currents going clockwise in my work. An attempt to do loop analysis has left me with the following equations:

i₄=(2V_x)/(1K)
i₁-i₂=8mA
i₃=-4mA
-i₂(4kΩ)=V_x

Upon solving for V₀, I got V₀=4.71V. Is this answer correct? If not, are my loop equations correct?

Please let me know if you guys want to see more work. Thanks!

 

[MisterX]

i₁-i₂=8mA

Check the value of the current source between loops 1 and 2.