. The sum of the greatest integer less than or equal to $x$ and the smallest integer greater than or equal to $x$ is 5, then the solution set of $x$ is
(A) $\{5 / 2\}$; (B) $\{x \mid 2 \leqslant x \leqslant 3\}$;
(C) $\{x \mid 2 \leqslant x<3\}$; (D) $\{x \mid 2<x \leqslant$
$3\}$; (E) $\{x \mid 2<x<3\}$.
7
$\mathrm{E}$
7. Let $\lfloor x\rfloor$ denote the greatest integer less than or equal to $x$, then $x-1<\lfloor x\rfloor \leqslant x, \cdots$ (1)

Let $\lceil x\rceil$ denote the smallest integer greater than or equal to $x$, then $x \leqslant\lceil x\rceil<x+1 \cdots$ (2).
It is also known that $\lfloor x\rfloor+\lceil x\rceil=5 \cdots(3)$
(1) + (2) $2 x-1<\lfloor x\rfloor+\lceil x\rceil<2 x+1$,

Substitute (3)
$2 x-1<5<2 x+1$ : Solving gives $2<x<3$.