Negative 11 can be visualized on a number line like this:
If we start at 0 and go 11 to the left, we get to negative 11. Now, to add negative 3, we go 3 more to the left, ending up even more negative than negative 11.
If we add positive 11 and negative 3, we start at 0 and go 11 to the right, then 3 to the left, ending up to the right of 0, but less positive than positive 11.
If we add two positives, we start at 0 and go 11 to the right, then 3 to the right, ending up even more positive than positive 11.
Now, let’s mark off the numbers on the number line and do the same problems again. If we add negative 11 and negative 3, we start at 0 and go 11 to the left, then 3 to the left, ending up at negative 14. I started at negative 11 and added negative 3, so I ended up at negative 14. To double check, I started at positive 11 and added positive 3, so I ended up at positive 14. Then, I started at negative 11 and added positive 3, so I ended up at negative 8. Lastly, I started at positive 11 and added negative 3, so I ended up at positive 8.