Решите уравнение: |x-4|+x=9.

Ответ:

\[|x - 4| + x = 9\]

\[\left\{ \begin{matrix} x - 4 + x = 9 \\ x - 4 > 0\ \ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} 2x = 13 \\ x > 4\ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x = 6,5 \\ x > 4\ \ \ \\ \end{matrix}\ \Longrightarrow \ x = 6,5 \right.\ \]

\[\left\{ \begin{matrix} - x + 4 + x = 9 \\ x - 4 < 0\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} 0 \cdot x = 5 \\ x < 4\ \ \ \ \\ \end{matrix}\ \Longrightarrow нет\ корней. \right.\ \]

\[Ответ:6,5,\]