Question

Giải bất ptt dạng tích: ( 3x-7 )( 4x-5 ) > 0

Answer 1

(3x-7)(4x-5)>0
TH1: \(\left\{{}\begin{matrix}3x-7>0\\4x-5>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>\dfrac{7}{3}\\x>\dfrac{5}{4}\end{matrix}\right.\Leftrightarrow x>\dfrac{7}{3}\)

TH2: \(\left\{{}\begin{matrix}3x-7< 0\\4x-5< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x< \dfrac{7}{3}\\x< \dfrac{5}{4}\end{matrix}\right.\Leftrightarrow x< \dfrac{5}{4}\)

Answer 2

\(\left(3x-7\right)\left(4x-5\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x-7>0\\4x-5>0\end{matrix}\right.\\\left\{{}\begin{matrix}3x-7< 0\\4x-5< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x>7\\4x>5\end{matrix}\right.\\\left\{{}\begin{matrix}3x< 7\\4x< 5\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\dfrac{7}{3}\\x>\dfrac{5}{4}\end{matrix}\right.\\\left\{{}\begin{matrix}x< \dfrac{7}{3}\\x< \dfrac{5}{4}\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{7}{3}\\x< \dfrac{5}{4}\end{matrix}\right.\)

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