a, ĐKXĐ : \(x^2+2\ne0\) ( luôn đúng với mọi x )
Ta có :\(\frac{3x-2}{x^2+2}\ge-1\)
=> \(\frac{3x-2}{x^2+2}+1\ge0\)
=> \(\frac{3x-2+x^2+2}{x^2+2}\ge0\)
=> \(x^2+3x\ge0\)
=> \(x\left(x+3\right)\ge0\)
=> \(\left[{}\begin{matrix}x\ge0\\x+3\ge0\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x\ge0\\x\ge-3\end{matrix}\right.\)
b, Ta có : \(\left|5x-9\right|\le6\)
TH1 : \(5x-9\ge0\left(x\ge\frac{9}{5}\right)\)
=> \(5x-9\le6\)
=> \(5x\le15\)
=> \(x\le3\)
=> \(\frac{9}{5}\le x\le3\)
TH2 : \(5x-9< 0\left(x< \frac{9}{5}\right)\)
=> \(9-5x\le6\)
=> \(-5x\le-3\)
=> \(x\ge\frac{3}{5}\)
=> \(\frac{3}{5}\le x< \frac{9}{5}\)
