Question

[Đức Lê Anh]

TÌM X BIẾT:\(\frac{2}{5}\)<\(|x-\frac{7}{5}|\)<\(\frac{3}{5}\)

Answer 1

[Phùng Minh Quân]

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

\(\Leftrightarrow\)\(\orbr{\begin{cases}\frac{2}{5}< x-\frac{7}{5}< \frac{3}{5}\\\frac{2}{5}>x-\frac{7}{5}>\frac{3}{5}\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}\frac{2}{5}+\frac{7}{5}< x-\frac{7}{5}+\frac{7}{5}< \frac{3}{5}+\frac{7}{5}\\\frac{2}{5}+\frac{7}{5}>x-\frac{7}{5}+\frac{7}{5}>\frac{3}{5}+\frac{7}{5}\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}\frac{9}{5}< x< 2\\\frac{9}{5}>x>2\end{cases}}\)

Vậy \(\frac{9}{5}< x< 2\) hoặc \(\frac{9}{5}>x>2\)

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