  We consider different notions of solutions to the $p(x)$-Laplace equation
$-\div(\abs{Du(x)}^{p(x)-2}Du(x))=0$ with $ 1<p(x)<\infty$. We show by proving
a comparison principle that viscosity supersolutions and $p(x)$-superharmonic
functions of nonlinear potential theory coincide. This implies that weak and
viscosity solutions are the same class of functions, and that viscosity
solutions to Dirichlet problems are unique. As an application, we prove a
Rad\'o type removability theorem.
