a. \(\left|\dfrac{5}{3}x\right|=\left|\dfrac{1}{6}\right|\)
\(\Rightarrow\left|\dfrac{5}{3}x\right|=\dfrac{1}{6}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{5}{3}x=\dfrac{1}{6}\\\dfrac{5}{3}x=\dfrac{-1}{6}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{10}\\x=\dfrac{-1}{15}\end{matrix}\right.\)
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b. \(\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|-\dfrac{3}{4}=\left|-\dfrac{3}{4}\right|\)
\(\Rightarrow\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|-\dfrac{3}{4}=\dfrac{3}{4}\)
\(\Rightarrow\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|=\dfrac{3}{4}+\dfrac{3}{4}\)
\(\Rightarrow\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|=\dfrac{3}{2}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{3}{4}x-\dfrac{3}{4}=\dfrac{3}{2}\\\dfrac{3}{4}x-\dfrac{3}{4}=\dfrac{-3}{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\dfrac{3}{4}x=\dfrac{9}{4}\\\dfrac{3}{4}x=\dfrac{-3}{4}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
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c. \(\left|x+\dfrac{3}{5}\right|-\left|x-\dfrac{7}{3}\right|=0\)
Để \(\left|x+\dfrac{3}{5}\right|-\left|x-\dfrac{7}{3}\right|=0\) thì
\(\Rightarrow\left\{{}\begin{matrix}\left|x+\dfrac{3}{5}\right|=0\\\left|x-\dfrac{7}{5}\right|=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x+\dfrac{3}{5}=0\\x-\dfrac{7}{5}=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-3}{5}\\x=\dfrac{7}{5}\end{matrix}\right.\) ( vô lí )
Vậy không có giá trị nào thỏa mãn.
