Tìm nghiệm chung của hai bất phương trình :\(\frac{{3x + 17}}{{10}} > \frac{{5x + 22}}{{15}}\,\,\left( 1 \right)\) và \(\frac{{x - 4}}{{30}} - 1 > \frac{{2x - 27}}{{24}}\,\,\left( 2 \right)\)

Ta có \(\frac{{3x + 17}}{{10}} > \frac{{5x + 22}}{{15}}\)

\(\begin{array}{l}\frac{{3\left( {3x + 17} \right)}}{{30}} > \frac{{2\left( {5x + 22} \right)}}{{30}}\\9x + 51 > 10x + 44\\9x - 10x > 44 - 51\end{array}\)

\(\begin{array}{l} - x >  - 7\\x < 7\left( {\rm{*}} \right)\end{array}\)

Ta có  \(\frac{{x - 4}}{{30}} - 1 > \frac{{2x - 27}}{{24}}\)

\(\begin{array}{l}\frac{{4\left( {x - 4} \right)}}{{120}} - \frac{{120}}{{120}} > \frac{{5\left( {2x - 27} \right)}}{{120}}\\4x - 16 - 120 > 10x - 135\end{array}\)

\(\begin{array}{l}4x - 10x > 16 + 120 - 135\\ - 6x > 1\end{array}\)

\(x <  - \frac{1}{6}\left( {{\rm{**}}} \right)\)