Решите уравнение: |x-1|+|x+2|=3.

\[|x - 1| + |x + 2| = 3\]

\[- (x - 1) - (x + 2) = 3\]

\[- x + 1 - x - 2 - 3 = 0\]

\[- 2x - 4 = 0\]

\[2x = - 4\]

\[x = - 2 \Longrightarrow \ \ не\ подходит.\]

\[- (x - 1) + x + 2 = 3\]

\[- x + 1 + x + 2 - 3 = 0\]

\[0 = 0\]

\[x \in \lbrack - 2;1)\]

\[x - 1 + x + 2 = 3\]

\[2x + 1 = 3\]

\[2x = 2\]

\[x = 1.\]

\[Ответ:\lbrack - 2;1\rbrack.\]