Centos – How to safely delete old kernel versions in CentOS 7

I might be encountering odd symptoms resulting from competing kernels in CentOS 7. So how do I safely delete the old kernels? And how do I know which kernel is the newest one?

Below is the terminal output I get at the moment when researching this on the server in question. Note that I tried package-cleanup but it leaves the same 2 kernels:

The instructions in this tutorial say that the output of the following two commands should match, but you can see that they do not match, even after a reboot:

[root@localhost ~]# rpm -qa kernel |sort -V |tail -n 1
kernel-3.10.0-229.el7.x86_64
[root@localhost ~]# uname -r
3.10.0-229.14.1.el7.x86_64

The remaining commands confirm that there are two kernels, and illustrate attempts to delete the old one.

[root@localhost ~]# cd /usr/src/kernels
[root@localhost kernels]# ls -al
total 16
drwxr-xr-x.  4 root root 4096 Oct  2 12:55 .
drwxr-xr-x.  4 root root 4096 Oct  2 13:15 ..
drwxr-xr-x. 22 root root 4096 Oct  2 12:55 3.10.0-229.14.1.el7.x86_64
drwxr-xr-x. 22 root root 4096 Oct  2 12:35 3.10.0-229.el7.x86_64
[root@localhost kernels]# rpm -q kernel
kernel-3.10.0-229.el7.x86_64
kernel-3.10.0-229.14.1.el7.x86_64
[root@localhost kernels]# package-cleanup --oldkernels=1
Loaded plugins: fastestmirror
Usage: 
    package-cleanup: helps find problems in the rpmdb of system and correct them

    usage: package-cleanup --problems or --leaves or --orphans or --oldkernels
Command line error: --oldkernels option does not take a value
[root@localhost kernels]# package-cleanup --oldkernels
Loaded plugins: fastestmirror
No old kernels to remove
[root@localhost kernels]# rpm -q kernel
kernel-3.10.0-229.el7.x86_64
kernel-3.10.0-229.14.1.el7.x86_64
[root@localhost kernels]# 

I also opened up /etc/yum.conf and set installonly_limit=1, but this resulted in an error from a subsequent yum update command saying that 1 is outside the range of acceptable values for installonly_limit.

I assume that 3.10.0-229.14.1.el7.x86_64 is the newest, but how can I know this? Also, the boot options seem to offer multiple kernels to choose from. And the opportunities for confusion get worse when the system auto-boots from the first kernel on the list of options.

Can someone please explain how this works, and in specific, how to safely delete old kernels so that kernel version can be eliminated as a possible cause of odd symptoms? I want to make sure that the most recent kernel is the only kernel that can ever run, no matter how the system is restarted.