1. Given the set
$$
M=\left\{x|5-| 2 x-3 \mid \in \mathbf{N}_{+}\right\} \text {. }
$$

Then the number of all non-empty proper subsets of $M$ is ( ).
(A) 254
(B) 255
(C) 510
(D) 511
- 1. C.

Given $5-|2 x-3| \in \mathbf{N}_{+}$, i.e., $|2 x-3|=0,1, 2,3,4$, we have
$$
M=\left\{-\frac{1}{2}, 0, \frac{1}{2}, 1, \frac{3}{2}, 2, \frac{5}{2}, 3, \frac{7}{2}\right\} .
$$

Since $M$ contains 9 elements, the number of all non-empty proper subsets of $M$ is $2^{9}-2=510$.