Question

\(\frac{-3}{7}< \frac{a}{5}< \frac{1}{3}\)

Answer 1

Ta có : \(\left\{{}\begin{matrix}-\frac{3}{7}< \frac{a}{5}\\\frac{a}{5}< \frac{1}{3}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}-\frac{3}{7}-\frac{a}{5}< 0\\\frac{a}{5}-\frac{1}{3}< 0\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{a}{5}+\frac{3}{7}>0\\\frac{a}{5}-\frac{1}{3}< 0\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{7a}{35}+\frac{15}{35}>0\\\frac{3a}{15}-\frac{5}{15}< 0\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}7a+15>0\\3a-5< 0\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}a>-\frac{15}{7}\\a< \frac{5}{3}\end{matrix}\right.\)

=> \(-\frac{15}{7}< a< \frac{5}{3}\)

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