The mysql service could not be started. The output error message of the mysql script was modified as follows:

$ /etc/init.d/mysql start
Starting MySQL database server: mysqld/usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
160811 10:54:23 mysqld_safe Logging to syslog.
160811 10:54:23 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql
160811 10:54:28 mysqld_safe mysqld from pid file /var/run/mysqld/mysqld.pid ended
/usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 ./usr/bin/mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
 failed!

Problem solving method:
according to the error message, we know that the cause of the problem is that the local IP cannot be accessed. Execute the ifconfig command:

bond0     Link encap:Ethernet  HWaddr fc:4d:d4:3d:1a:cf  
      inet addr:192.168.1.10  Bcast:192.168.1.255  Mask:255.255.255.0
      inet6 addr: fe80::fe4d:d4ff:fe3d:1acf/64 Scope:Link
      UP BROADCAST RUNNING MASTER MULTICAST  MTU:1500  Metric:1
      RX packets:220431 errors:0 dropped:0 overruns:0 frame:0
      TX packets:536525 errors:0 dropped:0 overruns:0 carrier:0
      collisions:0 txqueuelen:0 
      RX bytes:17535415 (16.7 MiB)  TX bytes:43680367 (41.6 MiB)

eth0      Link encap:Ethernet  HWaddr fc:4d:d4:3d:1a:cf  
      UP BROADCAST RUNNING SLAVE MULTICAST  MTU:1500  Metric:1
      RX packets:220431 errors:0 dropped:0 overruns:0 frame:0
      TX packets:536525 errors:0 dropped:0 overruns:0 carrier:0
      collisions:0 txqueuelen:1000 
      RX bytes:17535415 (16.7 MiB)  TX bytes:43680367 (41.6 MiB)
      Interrupt:20 Memory:fb300000-fb320000 

Ifconfig response shows that the local loopback device has not started. Execute “Ifconfig lo up” to pull up the local loopback device:

# ifconfig lo
lo        Link encap:Local Loopback  
      inet addr:127.0.0.1  Mask:255.0.0.0
      inet6 addr: ::1/128 Scope:Host
      UP LOOPBACK RUNNING  MTU:16436  Metric:1
      RX packets:0 errors:0 dropped:0 overruns:0 frame:0
      TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
      collisions:0 txqueuelen:0 
      RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)

Restart mysql service after the local loop device is pulled up:

$ /etc/init.d/mysql restart
Stopping MySQL database server: mysqld.
Starting MySQL database server: mysqld.

Another method is the entry “bind-address = 127.0.0.1” in the comment /etc/mysql/my.cnf file. Note: the bind-address entry is used to disable remote access to the mysql database, i.e. only allow local access.
port Settings that allow remote access:

# netstat -antp
Active Internet connections (servers and established)
Proto Recv-Q Send-Q Local Address           Foreign Address         State       PID/Program name
tcp        0      0 0.0.0.0:3306            0.0.0.0:*               LISTEN      29394/mysqld
...

Port Settings that allow local access only:

# netstat -antp
Active Internet connections (servers and established)
Proto Recv-Q Send-Q Local Address           Foreign Address         State       PID/Program name
tcp        0      0 127.0.0.1:3306          0.0.0.0:*               LISTEN      2657/mysqld
...

The second approach is not recommended for security reasons.