Решите уравнение: |8-|x+4||=7.

\[\left| 8 - |x + 4| \right| = 7\]

\[1)\ 8 - |x + 4| = 7\]

\[|x + 4| = 1\]

\[x + 4 = 1\]

\[x = - 3.\]

\[x + 4 = - 1\]

\[x = - 5.\]

\[2)\ 8 - |x + 4| = - 7\]

\[|x + 4| = 15\]

\[x + 4 = 15\]

\[x = 11.\]

\[x + 4 = - 15\]

\[x = - 19.\]

\[Ответ:\ - 19;\ - 5;\ - 3;11.\]