Will a seismic wave traveling through a solid go slower or faster than a seismic wave traveling through a liquid? Why?

You can't answer this question because you aren't giving the specific type of seismic waves. There is an s-wave a p-wave and an l-wave. Those are the basic waves. An S-wave cannot travel through a liquid at all. So, obviously it travels slower than any other seismic wave.

It would travel faster because their speed depends on the density and composition of material that they pass through.