Решите уравнение: |x+1|+|x-2|=3.

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

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

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

\[- 2x - 2 = 0\]

\[- 2x = 2\]

\[x = - 1.\]

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

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

\[0 = 0\]

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

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

\[2x - 1 = 3\]

\[2x = 4\]

\[x = 2\]

\[Ответ:\ \ \lbrack - 1;2\rbrack.\]