$4 \cdot 35$ The set of all real solutions to the inequality $| x-1|+| x+2 |<5$ is
(A) $\{x:-3<x<2\}$.
(B) $\{x:-1<x<2\}$.
(C) $\{x:-2<x<1\}$.
(D) $\left\{x:-\frac{3}{2}<x<\frac{7}{2}\right\}$.
(E) $\varnothing$ (empty set).
(24th American High School Mathematics Examination, 1973)
[Solution] (1) If $-20$, then the known inequality becomes $-x+1+x+21$, so $x-1>0$ and $x+2>0$, thus the known inequality becomes
$$
(x-1)+(x+2)=2 x+1-3$.
In summary, the set of real solutions is $-3<x<2$.
Therefore, the answer is $(A)$.