1. If $-2 \leqslant|x+1|-|a x-1| \leqslant 2$ holds for all $x \in$ $\mathbf{R}$, then the number of real numbers $a$ is ( ).
(A) 0
(B) 1
(C) 2
(D) infinitely many
-、1.C.
The original inequality always holds only when $a= \pm 1$.