a) \(\left|x-\dfrac{5}{3}\right|< \dfrac{1}{3}\)
\(\Rightarrow\dfrac{-1}{3}< x-\dfrac{5}{3}< \dfrac{1}{3}\)
\(\Rightarrow\dfrac{-1}{3}+\dfrac{5}{3}< x-\dfrac{5}{3}+\dfrac{5}{3}< \dfrac{1}{3}+\dfrac{5}{3}\)
\(\Rightarrow\dfrac{4}{3}< x< 2\)
b) \(\left|x+\dfrac{11}{2}\right|>\left|-5,5\right|=5,5\)
\(\Rightarrow\left\{{}\begin{matrix}x+\dfrac{11}{2}< 5,5\\x+\dfrac{11}{2}>5,5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 5,5-\dfrac{11}{2}=0\\x>5,5-\dfrac{11}{2}=0\end{matrix}\right.\)
=> Với x khác 0 thì thõa mãn đề bài
c) \(\dfrac{2}{5}< \left|x-\dfrac{7}{5}\right|< \dfrac{3}{5}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{2}{5}< x-\dfrac{7}{5}< \dfrac{3}{5}\\-\dfrac{2}{5}< x-\dfrac{7}{5}< -\dfrac{3}{5}\end{matrix}\right.\)
Ta thấy trường hợp 2 là trường hợp không thể xảy ra
=> Loại
Vậy \(\dfrac{2}{5}< x-\dfrac{7}{5}< \dfrac{3}{5}\)
\(\Rightarrow\dfrac{2}{5}+\dfrac{7}{5}< x< \dfrac{3}{5}+\dfrac{7}{5}\)
\(\Rightarrow\dfrac{9}{5}< x< 2\) (nhận)
p/s : làm đại nha , ko bik đúng sai
Làm theo công thức tổng quát:
a) \(\left|x\right|< m\Leftrightarrow-m\le x\le m\) (Tự làm)
b) \(\left|x\right|>m\Leftrightarrow\left[{}\begin{matrix}x>m\\x< -m\end{matrix}\right.\)
c) \(\dfrac{2}{5}< \left|x-\dfrac{7}{5}\right|< \dfrac{3}{5}\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x-\dfrac{7}{5}\right|>\dfrac{2}{5}\\\left|x-\dfrac{7}{5}\right|< \dfrac{3}{5}\end{matrix}\right.\)
+) TH1: \(\left|x-\dfrac{7}{5}\right|>\dfrac{2}{5}\Rightarrow\left[{}\begin{matrix}x-\dfrac{7}{5}>\dfrac{2}{5}\\x-\dfrac{7}{5}< -\dfrac{2}{5}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x>\dfrac{9}{5}\\x< 1\end{matrix}\right.\)
\(\Rightarrow\dfrac{9}{5}< x< 1\) (vô lí)
+) TH2: \(\left|x-\dfrac{7}{5}\right|< \dfrac{3}{5}\Rightarrow\dfrac{-3}{5}< x-\dfrac{7}{5}< \dfrac{3}{5}\)
Với \(x-\dfrac{7}{5}>\dfrac{-3}{5}\Rightarrow x>\dfrac{4}{5}\)
Với \(x-\dfrac{7}{5}< \dfrac{3}{5}\Rightarrow x< 2\)
Khi đó: \(\dfrac{4}{5}< x< 2\) (nhận)
Vậy \(\dfrac{4}{5}< x< 2.\)
