easy làm câu b vs c trước nha
b) \(\left(x-5\right)\left(2x+4\right)>0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-5>0\\2x+4>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-5< 0\\2x+4< 0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>5\\x>-2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 5\\x< -2\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>5\\x< -2\end{matrix}\right.\)
Vậy......
c) \(\left(x+3\right)\left(3x-6\right)< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+3>0\\3x-6< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+3< 0\\3x-6>0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-3\\x< 2\end{matrix}\right.\\\left\{{}\begin{matrix}x< -3\\x>2\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-3< x< 2\\x\in\varnothing\end{matrix}\right.\)
Vậy.......
Nốt câu a luôn nèk
\(\dfrac{x-12}{77}+\dfrac{x-11}{78}>\dfrac{x-74}{15}+\dfrac{x-73}{16}\)
\(\Leftrightarrow\left(\dfrac{x-12}{77}-1\right)+\left(\dfrac{x-11}{78}-1\right)>\left(\dfrac{x-74}{15}-1\right)+\left(\dfrac{x-73}{16}-1\right)\)\(\Leftrightarrow\dfrac{x-12-77}{77}+\dfrac{x-11-78}{78}>\dfrac{x-74-15}{15}+\dfrac{x-73-16}{16}\)\(\Leftrightarrow\dfrac{x-89}{77}+\dfrac{x-89}{78}>\dfrac{x-89}{15}+\dfrac{x-89}{16}\)\(\Leftrightarrow\dfrac{x-89}{77}+\dfrac{x-89}{78}-\dfrac{x-89}{15}-\dfrac{x-89}{16}>0\)\(\Leftrightarrow\left(x-89\right)\left(\dfrac{1}{77}+\dfrac{1}{78}-\dfrac{1}{15}-\dfrac{1}{16}\right)>0\)\(\Leftrightarrow x-89>0\)
\(\Leftrightarrow x>89\)
Hừm cx chưa chắc lắm
