I need to determine the voltage Vx assuming the linear operations. Any ideas???

 

hmm, Vx=-5V

 

The top opamp has a gain of 1.
The bottom opamp has a gain of 2.
The input is 5V.
Then the output is 10V.

But look. Both opamps have no power supply and are not biased. Then the output is nothing.

 

Any ideas???

There is an easy way to approach this problem. Call the noninverting input of the upper opamp ground. This allows all terminals on the upper input to be considered ground (assuming ideal opamps). Then, treat the 5 V supply as a -5V into the bottom opamp. The bottom opamp is a unity gain inverting amplifier, with ground at the noninverting terminal. Hence, the output of the lower opamp is +5V. This means that Vx, which is between the two opamp outputs is -5V.

Note that you will get this answer no matter where you assign a ground in the circuit, but this method is simple, since it allows you to do the problem in your head.

EDIT: I thought I would expand on Audioguru's approach, otherwise there may be confusion. Audoguru is equally correct to say the bottom opamp has a gain of +2 (rather than -1 as I said) because he is considering ground to be the negative terminal of the 5 V power supply. This is perfectly OK. I think when he says the output is 10V he means the output of the bottom opamp. However, I think Vx is supposed to be the difference between both opamp outputs. Hence the upper opamp has +5V out and the lower one has +10V out, but the difference is -5V.