a)\(\left|\dfrac{x-1}{3}\right|=\dfrac{11}{5}\Rightarrow\dfrac{x-1}{3}=\pm\dfrac{11}{5}\\ \Rightarrow\left[{}\begin{matrix}\dfrac{x-1}{3}=\dfrac{11}{5}\\\dfrac{x-1}{3}=-\dfrac{11}{5}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-1=\dfrac{33}{5}\\x-1=\dfrac{-33}{5}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{38}{5}\\x=\dfrac{-28}{5}\end{matrix}\right.\)
b)\(2\left|2x-3\right|=\dfrac{1}{2}\\ \Rightarrow\left|2x-3\right|=\dfrac{1}{4}\\ \Rightarrow2x-3=\pm\dfrac{1}{4}\\ \Rightarrow\left[{}\begin{matrix}2x-3=\dfrac{1}{4}\\2x-3=-\dfrac{1}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=\dfrac{13}{4}\\2x=\dfrac{-11}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{13}{8}\\x=\dfrac{-11}{8}\end{matrix}\right.\)
a: Ta có: \(\left|x-\dfrac{1}{3}\right|=\dfrac{11}{5}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{11}{5}\\x-\dfrac{1}{3}=-\dfrac{11}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{38}{15}\\x=-\dfrac{28}{15}\end{matrix}\right.\)
b: Ta có: \(2\left|2x-3\right|=\dfrac{1}{2}\)
\(\Leftrightarrow\left|2x-3\right|=\dfrac{1}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=\dfrac{1}{4}\\2x-3=-\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{13}{4}\\2x=\dfrac{11}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{13}{8}\\x=\dfrac{11}{8}\end{matrix}\right.\)
c: Ta có: \(2\left|3x-1\right|+1=5\)
\(\Leftrightarrow2\left|3x-1\right|=4\)
\(\Leftrightarrow\left|3x-1\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=2\\3x-1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=3\\3x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
d: Ta có: \(\dfrac{3}{2}+\dfrac{4}{5}\left|x-\dfrac{3}{4}\right|=\dfrac{7}{4}\)
\(\Leftrightarrow\dfrac{4}{5}\left|x-\dfrac{3}{4}\right|=\dfrac{1}{4}\)
\(\Leftrightarrow\left|x-\dfrac{3}{4}\right|=\dfrac{5}{16}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{5}{16}\\x-\dfrac{3}{4}=-\dfrac{5}{16}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{17}{16}\\x=\dfrac{7}{16}\end{matrix}\right.\)
e: Ta có: \(\left|2x-5\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-5=4\\2x-5=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=9\\2x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
f: Ta có: \(\left|\dfrac{1}{2}x-1\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x-1=3\\\dfrac{1}{2}x-1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=4\\\dfrac{1}{2}x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-4\end{matrix}\right.\)
