When you install an application package in a Debian-based system, sometimes prerequisite application packages are unavailable. These missing packages are known as broken dependencies.
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The two commands have several interfaces, including Aptitude, Synaptic, KPackage, Gnome-Apt, and dselect. Several of these interfaces, in particular Aptitude and dselect, include some of the tools you need for recovering from broken dependencies. However, as usually happens when an administrative problem arises on GNU/Linux, you have the widest set of options if you open a terminal while logged in as the root user and type the commands directly.