Question

Giá trị x > 0 thoả mãn: -7/3 < |2/7 - x| - 5/2 < -7/4

Answer 1

\(\Leftrightarrow-\dfrac{7}{3}+\dfrac{5}{2}< \left|x-\dfrac{2}{7}\right|< -\dfrac{7}{4}+\dfrac{5}{2}\)

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

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{6}< x-\dfrac{2}{7}< \dfrac{3}{4}\\-\dfrac{3}{4}< x-\dfrac{2}{7}< -\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{19}{42}< x< \dfrac{29}{28}\\-\dfrac{13}{28}< x< \dfrac{5}{42}\end{matrix}\right.\)

mà x>0

nên \(\left[{}\begin{matrix}\dfrac{19}{42}< x< \dfrac{29}{28}\\0< x< \dfrac{5}{42}\end{matrix}\right.\)