5. Solve the inequality $\frac{5 x+1}{x-3} \leq \frac{1}{3}$.
# Solution:

$\frac{5 x+1}{x-3} \leq \frac{1}{3}, \frac{5 x+1}{x-3}-\frac{1}{3} \leq 0, \frac{15 x+3-x+3}{3(x-3)} \leq 0, \frac{2(7 x+3)}{3(x-3)} \leq 0$

Answer: $\left[-\frac{3}{7} ; 3\right)$.

![](https://cdn.mathpix.com/cropped/2024_05_06_8eeeb8d6ace591217257g-10.jpg?height=211&width=580&top_left_y=1956&top_left_x=1452)