  Since the introduction of Askey-Wilson algebras by Zhedanov in 1991, the
classification of the finite-dimensional irreducible modules of Askey-Wilson
algebras remains open. A universal analog $\triangle_q$ of the Askey-Wilson
algebras was recently studied. In this paper, we consider a family of
infinite-dimensional $\triangle_q$-modules. By the universal property of these
$\triangle_q$-modules, we classify the finite-dimensional irreducible
$\triangle_q$-modules when $q$ is not a root of unity.
