<p>We consider the (generalized) absolute value equations with uncertain entries. In particular, we assume that the entries come from given intervals. For such interval-valued problem, we study the fundamental properties regarding solutions and solvability. First, we address the issue of the unique solvability of each realization. This is a hard problem, but it can be characterized by means of a regularity of a set of matrices or by a nonlinear system of inequalities; in contrast, the nonnegative unique solvability is polynomially decidable. Second, we focus on the overall solution set. We provide a closed-form characterization and inspect its topological properties such as boundedness. Since the solution set is hard to deal with, we derive a formula for an outer approximation and analyze the situation when the approximation is tight. Eventually, we investigate the convex hull of the solution set; we present an explicit formula that yields the convex hull under mild assumptions.</p>