Just to be clear, in general, just because coefficients change in response to adding more variables, does not mean we are doing a better job of constructing our model - as we see later in the course,for example, our estimators might become imprecise in certain situations. In this question however, I wouldn't worry too much about that. If you find that the coefficient changes, could it be that the new variables help us distill the unique effect of nox on median housing prices? Why might that be the case? What about those variables help us achieve that goal? That is one thing I would think about and consider, when answering the question.

To answer your question, I believe you are thinking about it in the right way, though you need to be careful of using words like "true effect" and "when x1 increases by 1 unit, y will change by XX units". The coefficient's meaning is tied to its size and direction (as well as significance, which is discussed later in the course). Imagine a very simple question; we are estimating the impact of class size (CS) on average test scores (Test Score). We are using data from 100 third-grade classes. Suppose we estimate that:

Test Score (hat) = 520.4 - 5.82*CS

Suppose we increase the size of a classroom from 19 to 20. What does our regression predict? Well, you can do this step by step:

Test Score (hat) = 520.4 - 5.82(19) = 409.82

Test Score (hat) = 520.4 - 5.82(20) = 404

What is the difference? -5.82. But that is just equivalent to the slope coefficient. We can say: the expected impact on the average test scores of a class, when we increase the class size by one student, is that it will decrease by 5.82 points. If we add more controls, we will need to clarify that our coefficient is the predicted effect of our variable of interest when we increase it by one unit, holding everything else constant. Remember, our model is built on a series of assumptions - and if those assumptions hold, this is what we would predict might happen.

Please let me know if that makes sense!