The Earth's inner core is solid because despite the enormous temperature in this region, there is also enormous pressure there, which in turn raises the melting point of iron and nickel to a value above the Earth's core temperature.
Now as we move out from the solid inner core, temperature drops, and pressure also decreases. Obviously because the inner core is solid but the outer core is liquid, we must conclude that the drop in temperature vs the drop in pressure must be lower than the gradient of 16 degrees/GPa shown in the diagram below (link to source), given that at the outer-core temperature has exceeded the melting point of iron/nickel, which is a function of pressure.
In other words, the drop in pressure must be quite significant compared to the drop in temperature as radius increases from the core.
So how is it that pressure drops off fast enough relative to temperature to give rise to the liquid outer-core. A good answer will explain how temperature drops off with radius and how pressure drops off with radius and how these compare to give rise to the liquid outer-core.