3 part connector means it is only designed for headphones (left, right, and ground).
4 part connector means it is designed for phones and mic (left, right ground and mic )
It is very difficult to tell how many segments the jack can accommodate because you can’t see in there.
Some spec pages state it has a headphone only jack, but the Dell page says it has a combo headphone and mic port (4 segment jack needed - like any old iphone or android phone).
It also has built in mics.
There is no “line out” port.
But headphones with a proper 4 segment jack should work.
There are adaptors available for three segment plugs into a 4 segment jack, because this combo doesn’t always line up perfectly. they run about 7 bucks on Amazon.
So check the plug and jack (preferably with a proper 4 segment plug).
Things to check:
Is there any bios settings that deal with audio?
What about the volume buttons on the right side?
Finally See this page: (ubuntu related) dealing with sound settings