Henry's constant and solubility
Actually solubility $x$ is given as a function of pressure $p$ and henry's constant $K_H$:
$$p=K_Hx$$


  My book says that higher the value of K at a given pressure lower is the solubility of the gas in the liquid. I don't understand how.


Since at a given pressure, $p$ is constant, if you increase $K_H$, logically solubility $x$ would decrease.