\(a,\left(x-3\right)^2< x^2-5x+4\\ \Leftrightarrow x^2-6x+9-x^2+5x-4< 0\\ \Leftrightarrow-x< -5\\ \Leftrightarrow x>5\\ S=\left\{x\in R|x>5\right\}\\ b,\left(x-3\right)\left(x+3\right)\le\left(x+2\right)^2+3\\ \Leftrightarrow x^2-9-x^2-4x-4-3\le0\\ \Leftrightarrow-4x-16\le0\\ \Leftrightarrow x\ge-4\\ S=\left\{x\in R|x\ge-4\right\}\)
\(c,\dfrac{4x-5}{3}>\dfrac{7-x}{5}\Leftrightarrow20x-25>21-3x\\ \Leftrightarrow23x>46\Leftrightarrow x>2\\ S=\left\{x\in R|x>2\right\}\\ d,\dfrac{2x+1}{2}+3\ge\dfrac{3-5x}{3}-\dfrac{4x+1}{4}\\ \Leftrightarrow12x+6+36\ge12-20x-12x-3\\ \Leftrightarrow44x\ge-33\Leftrightarrow x\ge-\dfrac{3}{4}\\ S=\left\{x\in R|x\ge-\dfrac{3}{4}\right\}\)
\(f,x^2-4x+3\ge0\\ \Leftrightarrow\left(x-3\right)\left(x-1\right)\ge0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3\ge0\\x-1\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x-3\le0\\x-1\le0\end{matrix}\right.\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x\ge3\\x\le1\end{matrix}\right.\\ S=\left\{x\in R|x\ge3;1\ge x\right\}\)
\(g,x^3-2x^2+3x-6< 0\\ \Leftrightarrow\left(x^2+3\right)\left(x-2\right)< 0\\ \Leftrightarrow x-2< 0\left(x^2+3>0\right)\\ \Leftrightarrow x< 2\\ S=\left\{x\in R|x< 2\right\}\\ h,\dfrac{x+2}{5}\ge0\Leftrightarrow x+2\ge0\left(5>0\right)\Leftrightarrow x\ge-2\\ S=\left\{x\in R|x\ge-2\right\}\)
\(i,\dfrac{x+2}{x-3}< 0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2>0\\x-3< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+2< 0\\x-3>0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-2\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< -2\\x>3\end{matrix}\right.\end{matrix}\right.\Leftrightarrow-2< x< 3\\ S=\left\{x\in R|-2< x< 3\right\}\)
