5) BPT \(\Leftrightarrow\dfrac{30x-45}{60}-\dfrac{20x+20}{60}>\dfrac{30}{60}-\dfrac{36-12x}{60}\)
\(\Leftrightarrow10x-65>12x-6\) \(\Leftrightarrow-2x>59\) \(\Leftrightarrow x< -\dfrac{59}{2}\)
Vậy ...
7) ĐK: \(x\ne-3\)
BPT \(\Leftrightarrow\dfrac{x+1}{x+3}-1>0\) \(\Leftrightarrow\dfrac{x+1}{x+3}-\dfrac{x+3}{x+3}>0\) \(\Leftrightarrow\dfrac{-2}{x+3}>0\)
\(\Rightarrow x+3< 0\) \(\Leftrightarrow x< -3\)
Vậy ...
9) Sửa đề: \(\dfrac{x^2+2x+2}{x^2+3}\ge1\)
\(\Leftrightarrow\dfrac{x^2+2x+2}{x^2+3}-1\ge0\) \(\Leftrightarrow\dfrac{x^2+2x+2}{x^2+3}-\dfrac{x^2+3}{x^2+3}\ge0\) \(\Leftrightarrow\dfrac{2x-1}{x^2+3}\ge0\)
\(\Rightarrow2x-1\ge0\) \(\Leftrightarrow x\ge\dfrac{1}{2}\)
Vậy ...
11) BPT \(\Leftrightarrow3x-2\le0\) \(\Leftrightarrow x\le\dfrac{2}{3}\)
Vậy ...
10) Ta có: \(\dfrac{2x+1}{x^2+2}\ge1\)
\(\Leftrightarrow\dfrac{2x+1-x^2-2}{x^2+2}\ge0\)
\(\Leftrightarrow-x^2+2x-1\ge0\)
\(\Leftrightarrow x^2-2x+1\le0\)
\(\Leftrightarrow x=1\)
12) Ta có: \(\left(x-2\right)\left(x+1\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-2\right)\left(x+1\right)>0\\\left(x-2\right)\left(x+1\right)=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x-2>0\\x+1< 0\end{matrix}\right.\\\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x>2\\x< -1\end{matrix}\right.\\\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge2\\x\le-1\end{matrix}\right.\)
