Linux mint doesn't boot after installing in old macbook 2007 white

After installing Linux mint with LVM in all disk space in **macbook 2007**, I installed this linux with guided installation, during installation i choosed **erase disk and knstall**, for advanced features i choosed **LVM installation** Ifter installation completed I tried to restart the system for the first time and it cand boot ! Juste a gray screen and a directory climbing with interrogation mark After booting with a Linux live I get this information about macbooc hdd From gparted From disk Where is the problem ! There is a boot esp partition, and lvm partition for filesystem