다음을 풀어보세요: {l}{(m+n)x+3m-2n<0}{x>-1/2}

$$\left. \begin{array} { l } { ( m + n ) x + 3 m - 2 n < 0 } \\ { x > - \frac { 1 } { 2 } } \end{array} \right.$$

x에 대한 해

$$\left\{\begin{matrix}x>-\frac{1}{2}\text{, }&\left(n>0\text{ and }m=-n\right)\text{ or }\left(|m|>|n|\text{ and }m<-n\right)\\x>-\frac{3m-2n}{m+n}\text{, }&m\geq n\text{ and }m<-n\\x\in \left(-\frac{1}{2},-\frac{3m-2n}{m+n}\right)\text{, }&|n|>|m|\text{ and }m>-n\end{matrix}\right.$$

n에 대한 해

$$\left\{\begin{matrix}n>-\frac{m\left(x+3\right)}{x-2}\text{, }&x>-\frac{1}{2}\text{ and }x<2\\n\in \mathrm{R}\text{, }&x=2\text{ and }m<0\\n<-\frac{m\left(x+3\right)}{x-2}\text{, }&x>2\end{matrix}\right.$$