-2sin(П+3x)<=sqrt3. тригонометрия.

[tex]-2\sin( \pi +3x) \leq \sqrt{3} |:(-2)\\ \sin( \pi +3x) \geq - \frac{\sqrt{3}}{2} \\ - \frac{\pi}{3} +2 \pi n \leq \pi +3x \leq \frac{4 \pi }{3} +2 \pi n,n\in \mathbb{Z}\,\,\,\,\, \big|- \pi \\ \\ -\frac{4\pi}{3} +2 \pi n \leq 3x \leq \frac{\pi}{3} +2 \pi n,n \in \mathbb{Z}\,\,\,\,\,\, \big|:3\\ \\ \boxed{-\frac{4\pi}{9}+\frac{2\pi n}{3} \leq x \leq \frac{\pi}{9}+\frac{2\pi n}{3} ,n \in \mathbb{Z} }[/tex]