2. The integer solutions of the inequality $0 \leqslant a x+5 \leqslant 4$ are 1, 2, 3, 4. Then the range of values for $a$ is ( ).
(A) $a \leqslant-\frac{5}{4}$
(B) $a<-1$
(C) $-\frac{5}{4} \leqslant a<-1$
(D) $a \geqslant-\frac{5}{4}$
2.C.

It is known that $-\frac{1}{a} \leqslant x \leqslant-\frac{5}{a}$.
According to the problem, we should have
$$
\begin{array}{l}
0-\frac{5}{a} \geqslant 4 . \\
\text { Therefore, }-\frac{5}{4} \leqslant a<-1 .
\end{array}
$$