Решите неравенство: корень из (2x-6)<=2.

\[\sqrt{2x - 6} \leq 2\]

\[t = 2x - 6\]

\[\sqrt{t} \leq 2 \Longrightarrow 0 \leq t \leq 4 \Longrightarrow\]

\[\Longrightarrow 0 \leq 2x - 6 \leq 4\ \]

\[\left\{ \begin{matrix} 2x - 6 \geq 0 \\ 2x - 6 \leq 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2x \geq 6\ \ \\ 2x \leq 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x \geq 3 \\ x \leq 5 \\ \end{matrix} \right.\ \]

\[Ответ:\lbrack 3;5\rbrack\text{.\ }\]