Is the Endpoint In?

The dot at the endpoint shows whether the endpoint is a solution. $3x+1 \le 7$ solves to $x \le 2$. The sign is ≤, so the number 2 itself is a solution. Check it: $3\cdot 2+1 = 7$, and 7 is less than or equal to 7. So the dot at 2 is filled.

3x + 1 ≤ 7, that is x ≤ 2: a filled dot at 2

A strict sign gives an open dot. For example, $3x+1 < 7$ has the same endpoint, 2, but now 2 is not a solution, because 7 is not less than 7. So the dot at 2 is open. Only the sign of the solved inequality decides whether the dot is filled or open.