Решите уравнение: |x-1|-|x-7|=8.

\[|x - 1| - |x - 7| = 8\]

\[1)\ \left\{ \begin{matrix} x < 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 1 - x - 7 + x = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} x < 1\ \ \ \ \ \ \ \ \\ 0 \cdot x = 14 \\ \end{matrix} \right.\ \ \ \ \ \ нет\ корней\]

\[2)\ \left\{ \begin{matrix} 1 \leq x \leq 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - 1 - 7 + x = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} 1 \leq x \leq 7 \\ 2x = 16\ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} x = 8\ \ \ \ \ \ \ \ \\ 1 \leq x \leq 7 \\ \end{matrix} \right.\ \ \ \ \ нет\ корней\]

\[3)\ \left\{ \begin{matrix} x > 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - 1 - x + 7 = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x > 7\ \ \ \ \ \\ 0 \cdot x = 2 \\ \end{matrix} \right.\ \ \ \ \ \ \ нет\ корней\]

\[Ответ:\ нет\ корней.\]