Question

Tìm x biết 2/5<|x-7/5|<3/5

Answer 1

Ta có: \(\frac{2}{5}< \left|x-\frac{7}{5}\right|< \frac{3}{5}\)

\(\Leftrightarrow\left[{}\begin{matrix}\frac{2}{5}< x-\frac{7}{5}< \frac{3}{5}\\\frac{2}{5}< \frac{7}{5}-x< \frac{3}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\frac{2}{5}+\frac{7}{5}< x-\frac{7}{5}+\frac{7}{5}< \frac{3}{5}+\frac{7}{5}\\\frac{2}{5}-\frac{7}{5}< \frac{7}{5}-x-\frac{7}{5}< \frac{3}{5}-\frac{7}{5}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\frac{9}{5}< x< 2\\-1< -x< -\frac{4}{5}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\frac{9}{5}< x< 2\\1>x>\frac{4}{5}\end{matrix}\right.\)

Vậy: S={x|\(\left[{}\begin{matrix}\frac{9}{5}< x< 2\\1>x>\frac{4}{5}\end{matrix}\right.\)}