\(x< -2\Rightarrow\left|x+2\right|+\left|x-3\right|=-x-2+3-x=1-2x\)
\(\Rightarrow\left\{{}\begin{matrix}x< -2\\1-2x\ge10x-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< -2\\x\le\dfrac{1}{4}\end{matrix}\right.\)\(\Leftrightarrow x< -2\left(1\right)\)
\(-2\le x< 3\Rightarrow\left|x+2\right|+\left|x-3\right|=x+2+3-x=5\Rightarrow\left\{{}\begin{matrix}-2\le x< 3\\5\ge10x-2\Leftrightarrow x\le\dfrac{7}{10}\end{matrix}\right.\)
\(\Leftrightarrow-2\le x\le\dfrac{7}{10}\left(2\right)\)
\(x\ge3\Rightarrow\left|x+2\right|+\left|x-3\right|=x+2+x-3=2x-1\Rightarrow\left\{{}\begin{matrix}x\ge3\\2x-1\ge10x-2\Leftrightarrow x\le\dfrac{1}{8}\end{matrix}\right.\)
\(\Rightarrow x\in\phi\)
\(\left(1\right)\left(2\right)\Rightarrow x\in\phi\)
