Using aptitude for package management instead of apt-get, please note that it is bad practice to use aptitude and apt-get interchangeably, as they record separately the changes made by a user.
Open the Terminal from the Mint Menu and start with the commands:
sudo aptitude update && sudo aptitude install gtkorphan
The && is used to run the second command if the first command runs successfully.
Continue by running:
sudo aptitude update && sudo aptitude upgrade
This is used to double-check that you have all the updates.
To clear out the broken packages use the command:
sudo aptitude -f
It brings up a beautiful interface to search, navigate, install, update and otherwise to manage packages.
Use the commands on the screen to install all the updates. You may use the mouse or CTRL + T to open the menu. Also, you could use the arrow keys and the Enter key to navigate.
You can also install the Aptitude Package Manager if you want to use something like Synaptic. Just type aptitude-gtk in the search field of the Mint Menu and click on Install package 'aptitude-gtk'. You can then find it under the Administration menu.
You may also use other commands to:
install software for your system, with needed dependencies as well:
sudo aptitude install
remove packages as well as orphaned dependencies:
sudo aptitude remove
remove packages and orphaned dependencies, as well as any configuration files left behind:
sudo aptitude purge
search for packages in the local apt package lists:
sudo aptitude search package-name
show details about a package:
sudo aptitude show package-name
update the local packages lists:
sudo aptitude update
upgrade any installed packages that have been updated:
sudo aptitude upgrade
upgrade packages, even if it means uninstalling certain packages:
sudo aptitude dist-upgrade
delete only out-of-date packages, but keep current ones:
sudo aptitude autoclean
delete any downloaded files necessary for installing the software on your system:
sudo aptitude clean
fix a package at it’s current version, and don’t update it:
sudo aptitude hold