Not enough space to install apt packages/how do I resize /var/?

Clearing the apt packages cache does not help, neither do I have any extra update packages. Whenever I try to apt install something, it tells me I have no space left. df -h says my /var/ is full, so I'm trying to resize it, but neither fdisk or lvextend seem to work. Do I need a reinstall? edit: df output

Filesystem       Size  Used Avail Use% Mounted on
udev             7.8G     0  7.8G   0% /dev
tmpfs            1.6G  1.8M  1.6G   1% /run
/dev/nvme0n1p6    23G   15G  7.3G  67% /
tmpfs            7.8G     0  7.8G   0% /dev/shm
tmpfs            5.0M     0  5.0M   0% /run/lock
/dev/nvme0n1p9   1.8G  156K  1.7G   1% /tmp
/dev/nvme0n1p7   9.1G  8.6G   23M 100% /var
/dev/nvme0n1p10  864G   46G  775G   6% /home
tmpfs            1.6G   80K  1.6G   1% /run/user/1000