Difference between +x and a+x in chmod

+x depends on umask:

$ umask 007
$ touch file
$ ls -la file 
-rw-rw---- 1 dmitritelinov dmitritelinov 0 Jul 31 23:29 file
$ chmod -v +x file 
mode of 'file' changed from 0660 (rw-rw----) to 0770 (rwxrwx---)

while a+x applies changes regardless of umask:

$ chmod -v a+x file 
mode of 'file' changed from 0770 (rwxrwx---) to 0771 (rwxrwx--x)