We know when we're doing the mesh analysis,

and using this solution, approach for our problem.

We are finding the mesh currents.

So the first thing that we do for

mesh analysis is we assign the meshes and the mesh currents.

Ultimately, what we get from our

mesh analysis is the value for

each of the mesh currents, I1, I2 and I sub 3.

Once we know those three currents, we can find any other

value of interest for any of the elements in the circuit.

We can find the currents, we can find the voltages,

we can find the power that's absorb nor supplied by each of those elements.

In this case, what we're looking for is V out.

So with regard to mesh analysis,

V out is simply going to be 6 kilo ohms times the mesh current I sub 2.

If we can find I sub 2, then we can find V out because we know that V out for

mesh analysis is going to be I sub 2 times 6K.

So let's start with mesh one and let's add our voltages up