Question

Giá trị x > 0 nguyên thỏa mãn \(\frac{-7}{3}< \left|\frac{2}{7}-x\right|-\frac{5}{2}< \frac{-7}{4}\)

giúp mk mn ơi !!!!!!!

Answer 1

\(\Leftrightarrow\dfrac{1}{6}< \left|\dfrac{2}{7}-x\right|< \dfrac{3}{4}\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left|x-\dfrac{2}{7}\right|>\dfrac{1}{6}\\\left|x-\dfrac{2}{7}\right|< \dfrac{3}{4}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in\left(-\infty;\dfrac{10}{84}\right)\cup\left(\dfrac{38}{84};+\infty\right)\\x\in\left(-\dfrac{39}{84};\dfrac{87}{84}\right)\end{matrix}\right.\)

\(\Leftrightarrow x\in\left(\dfrac{38}{84};\dfrac{87}{84}\right)\)