Considering all values of x and y for which x+y is at most 7, x is at least 2, and y is at least -1, what is the minimum value of y-2x?

Since x+y is at most 7 and y is at least -1, x is at most 8.

The minimum value of y - 2x happens when y has its lowest value (-1) and x has its highest value, which we just decided is 8. Therefore
y - 2x > -17