Question

[Angels of Death]

Tìm x

2/5 < Ix - 7/5I < 3/5

Answer 1

[Ngô Chi Lan]

Bài làm:

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

\(\Leftrightarrow\frac{2}{5}< x-\frac{7}{5}< \frac{3}{5}\)

\(\Leftrightarrow\frac{9}{5}< x< 2\)

Answer 2

[Fudo]

                                                      Bài giải

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

Có 2 trường hợp :

TH1 : \(x-\frac{7}{5}< 0\)\(\Rightarrow\text{ }x< \frac{7}{5}\)

\(\Rightarrow\text{ }\frac{2}{5}< -x+\frac{7}{5}< \frac{3}{5}\)

\(\Rightarrow\text{ }\frac{2}{5}-\frac{7}{5}< -x+\frac{7}{5}-\frac{7}{5}< \frac{3}{5}-\frac{7}{5}\)

\(\Rightarrow\text{ }-1< -x< -\frac{4}{5}\) ( loại ) 

TH2 : \(x-\frac{7}{5}\ge0\text{ }\Rightarrow\text{ }x\ge\frac{7}{5}\)

\(\Rightarrow\text{ }\frac{2}{5}< x-\frac{7}{5}< \frac{3}{5}\)

\(\Rightarrow\text{ }\frac{2}{5}+\frac{7}{5}< x-\frac{7}{5}+\frac{7}{5}< \frac{3}{5}+\frac{7}{5}\)

\(\Rightarrow\text{ }\frac{9}{5}< x< 2\)

\(\Rightarrow\text{ }1,8< x< 2\)