Should x > 0 have a open or closed dot

Open

Step-by-step explanation:

We use open circles to represent a value not included, and closed circles to represent an included value.

Since this is x is less than 0, not x is less than or equal to 0, we don't use a closed circle. We want to make it clear that we're not including 0 in the line!

an open dot

Step-by-step explanation:

if the signs are > or < the dot is open

if the signs are ≥ or ≤ the dot is closed