$2 \cdot 82$ Given $|x-1|+|x-5|=4$, then the range of $x$ is
(A) $1 \leqslant x \leqslant 5$.
(B) $x \leqslant 1$.
(C) $1<x<5$.
(D) $x \geqslant 5$.
(Mathematics League of Junior High Schools in Guangzhou, Wuhan, Fuzhou, and other five cities, 1985)
［Solution］Substitute the given $x$ values into the equation, the result is:
According to $(B)$ and $(D)$, if we take $x=0$ or $x=6$, the equation does not hold; if we substitute $x=1$ (or $x=5$) into the equation, it holds. Therefore, $(C): 1<x<5$ does not apply. Hence, the answer is $(A)$.