\(\Rightarrow\frac{7}{6}< |x-\frac{2}{3}|< \frac{26}{9}\)

\(\Rightarrow\frac{21}{18}< |x-\frac{2}{3}|< \frac{52}{18}\)

Rùi tự thay vào 

\(\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\)

\(\Leftrightarrow\frac{7}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{9}\)

\(\Leftrightarrow\frac{7}{6}< 2\le\left|x-\frac{2}{3}\right|\le2< \frac{26}{9}\)

\(\Leftrightarrow\left|x-\frac{2}{3}\right|=2\)

\(\Leftrightarrow\orbr{\begin{cases}x-\frac{2}{3}=2\\x-\frac{2}{3}=-2\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{8}{3}\\x=--\frac{4}{3}\end{cases}}\)

Vậy \(x\in\left\{\frac{8}{3};-\frac{4}{3}\right\}\)

- Ta có : \(\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\)

=> \(\left\{{}\begin{matrix}\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|\\\left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{7}{6}< \left|x-\frac{2}{3}\right|\\\left|x-\frac{2}{3}\right|< \frac{26}{9}\end{matrix}\right.\)

- TH₁ : \(x-\frac{2}{3}\ge0\left(x\ge\frac{2}{3}\right)\)

=> \(\left\{{}\begin{matrix}\frac{7}{6}< x-\frac{2}{3}\\x-\frac{2}{3}< \frac{26}{9}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{11}{6}< x\\x< \frac{32}{9}\end{matrix}\right.\)

=> \(\frac{11}{6}< x< \frac{32}{9}\)

Mà x là số nguyên .

=> \(x\in\left\{2,3\right\}\)

- TH₂ : \(x-\frac{2}{3}< 0\left(x< \frac{2}{3}\right)\)

=> \(\left\{{}\begin{matrix}\frac{7}{6}< \frac{2}{3}-x\\\frac{2}{3}-x< \frac{26}{9}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}\frac{1}{2}< -x\\-x< \frac{20}{9}\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}-\frac{1}{2}>x\\x>-\frac{20}{9}\end{matrix}\right.\)

=> \(-\frac{1}{2}>x>-\frac{20}{9}\)

Mà x là số nguyên .

=> \(x\in\left\{-1,-2\right\}\)

I là tham số à bạn

\(\frac{7}{6}< |a-\frac{2}{3}|< \frac{26}{9}\Leftrightarrow\frac{21}{18}< |a-\frac{2}{3}|< \frac{52}{18}\Leftrightarrow\orbr{\begin{cases}-\frac{52}{18}< a-\frac{2}{3}< -\frac{21}{18}\\\frac{21}{18}< a-\frac{2}{3}< \frac{52}{18}\end{cases}}\) 

giai tiếp nha bạn

Do \(\left|x-\dfrac{2}{3}\right|\ge0;\forall x\)

Mà \(-\dfrac{26}{\sqrt{81}}< 0\)

\(\Rightarrow\) Không tồn tại x để \(\left|x-\dfrac{2}{3}\right|< -\dfrac{26}{\sqrt{81}}\)

Hay ko tồn tại số nguyên x thỏa mãn đề bài

\(\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\)

\(\Rightarrow\frac{7}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{9}\)

\(\Rightarrow\frac{21}{18}< \left|x-\frac{12}{18}\right|< \frac{52}{18}\)

còn lại cậu tự tính nha

\(\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\)

\(\frac{7}{6}< x-\frac{2}{3}< \frac{26}{9}\)

\(\frac{11}{6}< x< \frac{32}{9}\)