  In this article, we construct explicit meromorphic solutions of first order
linear $q$-difference equations in the complex domain and we describe the
location of all their zeros and poles. The homogeneous case leans on the study
of four fundamental equations, providing the previous informations in the
framework of entire or meromorphic coefficients. The inhomogeneous situation,
which stems from the homogeneous one and two fundamental equations, is also
described in detail. We also address the case of higher-order linear
$q$-difference equations, using a classical factorization argument. All these
results are illustrated by several examples.
