What happens when the density of a medium increases

We all know that the sound travels faster through solids and then liquids and then through gases.

As far as i know solids are the medium through which the sound travels fast.

But in some websites I saw that as the density increases, the velocity of the sound decreases. If this statement is correct, how come the sound travels fastest through solids (since they have higher density)

From this it is clear that not only sound as compression wave But also in the form of Shear wave travels in Solids

This makes it easier for sound to travel with higher speed in solids