  We consider the $\gamma$-Liouville quantum gravity (LQG) model for $\gamma
\in (0,2)$, formally described by $e^{\gamma h}$ where $h$ is a Gaussian free
field on a planar domain $D$. Sheffield showed that when a certain type of LQG
surface, called a quantum wedge, is decorated by an appropriate independent SLE
curve, the wedge is cut into two independent surfaces which are themselves
quantum wedges, and that the original surface can be recovered as a unique
conformal welding. We prove that the original surface can also be obtained as a
metric space quotient of the two wedges, extending results of Gwynne and Miller
in the special case $\gamma = \sqrt{8/3}$ to the whole subcritical regime
$\gamma \in (0,2)$.
  Since the proof for $\gamma = \sqrt{8/3}$ used estimates for Brownian
surfaces, which are equivalent to $\gamma$-LQG surfaces only when
$\gamma=\sqrt{8/3}$, we instead use GFF techniques to establish estimates
relating distances, areas and boundary lengths, as well as bi-H\"{o}lder
continuity of the LQG metric w.r.t. the Euclidean metric at the boundary, which
may be of independent interest.
