# What the R value to this operational amplifier isn't saturated?

In the following circuit, the three ideal operational amplifiers are polarized such that their saturation voltages are ± 20 VDC. The other components of the circuit are resistors, one of them being adjustable (the Rx).

What is the limit condition for adjusting Rx so that the output voltage does not saturate?

A) 3kΩ < Rx < 4 kΩ. B) Rx > 5 kΩ. C) Rx < 5 kΩ. D) 4 kΩ < Rx < 5 kΩ. E) Rx < 4 kΩ.

My attempt:

Consider $$\V_{down}\$$ and $$\V_{up}\$$ the voltage on Buffers inputs are $$\\frac{40}{3}V\$$ and $$\\frac{20}{R_x + 1}V\$$ respectively.

So the Summing Amplifier is:

$$V_{out} = -2k\left(\frac{\frac{20}{R_x+1}}{1k}+\frac{\frac{40}{3}}{2k}\right)$$

Consider that $$\V_{out} \leq -20V\$$ (I'm not for sure this statement)

$$-20 \geq -2k\left(\frac{\frac{20}{R_x+1}}{1k}+\frac{\frac{40}{3}}{2k}\right)\Rightarrow 10 \leq \frac{20}{Rx+1}+\frac{20}{3}\Rightarrow \frac{1}{Rx+1}+\frac{1}{3} \geq \frac{1}{2}\\ \frac{6}{Rx+1}+2 \geq 3\Rightarrow 6\geq R_x+1\Rightarrow R_x \leq 5k\Omega$$

I find the letter C) but the correct answer is letter B).

What did I miss?