Stuck on a simple piecewise linear element problem
One possible way is to use a Thevenin's theorem and replace this circuit with the equivalent circuit that contains only a single RTH resistor and nonlinear element in series with the RTH resistor and Vth voltage source.

And use the load line to find the operation point.  

https://www.allaboutcircuits.com/technical-articles/how-is-a-load-line-used-in-circuit-design/   

The equivalent circuit will look like this: 



Where: 

$$V_{TH} = V_S \times \frac{R_P}{R_S + R_2} \approx 2.76V$$

$$R_{TH} =R_S||R_P \approx 2.6k\Omega$$

All this means that the current that flows through a nonlinear element cannot be greater than this:
$$I = \frac{V_{TH}}{R_{TH}} \approx 1.06mA $$