3. From the five numbers $-3, -2, \frac{1}{2}, 1, 3$, a number is randomly selected and denoted as $a$. If the number $a$ makes the system of inequalities
$$
\left\{\begin{array}{l}
\frac{1}{3}(2 x+7) \geqslant 3, \\
x-a<0
\end{array}\right.
$$

have no solution, and makes the fractional equation
$$
\frac{x}{x-3}-\frac{a-2}{3-x}=-1
$$

have a positive integer solution, then the sum of all values of $a$ that satisfy the conditions among these five numbers is ( ).
(A) -5
(B) -2
(C) 1
(D) $\frac{3}{2}$
3. B.

From the given system of inequalities, we get $x \geqslant 1$ and $x < a$. Since the system of inequalities has no solution, we know $a \leqslant 1$.
From $\frac{x}{x-3}-\frac{a-2}{3-x}=-1$, we get $x=\frac{5-a}{2}$.
Since $x=\frac{5-a}{2}$ is a positive integer, and $a \leqslant 1$, thus, $a=-3$ or 1.
Therefore, the answer is -2.