Решите уравнение: |x-2|+x=8.

Ответ:

\[|x - 2| + x = 8\ \]

\[\left\{ \begin{matrix} x - 2 + x = 8 \\ x - 2 \geq 0\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2x = 10 \\ x \geq 2\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 5 \\ x \geq 2 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - x + 2 + x = 8 \\ x - 2 < 0\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 0 \cdot x = 6 \\ x < 2\ \ \ \ \ \ \\ \end{matrix} \right.\ ,\ нет\ корней\]

\[Ответ:5.\]