`~rai~`
\(sin\left(2x-\dfrac{\pi}{6}\right)=sin\left(x+\dfrac{\pi}{3}\right)\\\Leftrightarrow \left[\begin{array}{I}2x-\dfrac{\pi}{6}=x+\dfrac{\pi}{3}+k2\pi\\2x-\dfrac{\pi}{6}=\pi-x-\dfrac{\pi}{3}+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x_{1}=\dfrac{\pi}{2}+k2\pi\\x_{2}=\dfrac{5\pi}{18}+k\dfrac{2\pi}{3}.\end{array}\right.\quad(k\in\mathbb{Z})\\Vì\quad |x|\le 2\Leftrightarrow -2\le x\le 2.\\TH1:-2\le x_{1}\le 2\\\Leftrightarrow -2\le \dfrac{\pi}{2}+k2\pi\le 2\\\Leftrightarrow -0,5683...\le k\le0,0683...\\Mà \quad k\in\mathbb{Z}\Rightarrow k=0\Rightarrow x=\dfrac{\pi}{2}.\\TH2:-2\le x_{2}\le 2\\\Leftrightarrow -2\le \dfrac{5\pi}{18}+k\dfrac{2\pi}{3}\le 2\\\Leftrightarrow -1,37159...\le k\le 0,53826...\\Mà\quad k\in\mathbb{Z}\Rightarrow k\in\{-1;0\}\\\Rightarrow x=-\dfrac{7\pi}{18};x=\dfrac{5\pi}{18}.\\\text{Vậy phương trình có 3 nghiệm x thỏa mãn |x|}\le 2\quad là:\\x=\dfrac{\pi}{2};x=-\dfrac{7\pi}{18};x=\dfrac{5\pi}{18}.\)
