Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)
Each term will be -1 < term value < 0
So the floor for each will be -1
Sum = 1000 (-1) = -1000
+12 
