Determine the power absorbed by element 1.
We will find power for each element in terms of I_x and then solve for I_x at the end. Remember that current multiplied by the voltage gives us power.
In the circuit, all power absorbed must equal the power supplied. In our case, three sources supply power (the elements with negative power values), and the power absorbed by the two other elements must equal each other. In other words, if we add all of the power together, the ones that supply power and absorb power, it must all equal to 0. Thus, we can write the following equation:
now, we can solve to find the power absorbed by element 1: