Finding Voltage at D and Potential Difference Between B & E

[zorro]

Homework Statement

What is the voltage at D ? What is the the potential difference between B and E?

The Attempt at a Solution

The point D is connected to +6V and -3 V . So the effecting voltage at D is 3 V.
But the answer is -3 V.

For calculating the potential difference, I found out currents in all branches using KLR and JR.
Is there any shorter method without finding out the currents?

 

[gneill]

Pay careful attention to the polarities of the batteries.

If you "walk" the loop from B to C to D to E, what's the change in potential?

 

[zorro]

From B to C, there is Vc - Vb = -3V and Ve-Vc=-6V (is it right?)
adding them Ve-Vb = -9V
so Vb-Ve = 9V

That answers my second question.
What about the first?

 

[gneill]

That answers my second question.
What about the first?

You passed by the answer when you "walked" from B to D!

"Walk" the loop from A to B to C to D.

 

[zorro]

I got it now.
Thanks!