Решите уравнение: ||x+1|-4|=3.

\[\left| |x + 1| - 4 \right| = 3\]

\[1)\ |x + 1| - 4 = 3\]

\[|x + 1| = 7\]

\[x + 1 = 7\]

\[x = 6.\]

\[x + 1 = - 7\]

\[x = - 8.\]

\[2)\ |x + 1| - 4 = - 3\]

\[|x + 1| = 1\]

\[x + 1 = 1\]

\[x = 0.\]

\[x + 1 = - 1\]

\[x = - 2.\]

\[Ответ:\ - 8; - 2;0;6.\]