Решите неравенство: корень из (5x-1)<=3.

\[\sqrt{5x - 1} \leq 3\ \ \]

\[t = 5x - 1\]

\[\sqrt{t} \leq 3 \Longrightarrow 0 \leq t \leq 9 \Longrightarrow\]

\[\Longrightarrow 0 \leq 5x - 1 \leq 9\]

\[\left\{ \begin{matrix} 5x - 1 \geq 0 \\ 5x - 1 \leq 9 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 5x \geq 1\ \ \\ 5x \leq 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x \geq \frac{1}{5} \\ x \leq 2 \\ \end{matrix} \right.\ \]

\[Ответ:\lbrack 0,2;2\rbrack\text{.\ }\]