a: =>|x-19/5|=2
=>x-19/5=2 hoặc x-19/5=-2
=>x=29/5 hoặc x=9/5
b: =>|3x+1|-11=3 hoặc |3x+1|-11=-3
=>|3x+1|=14 hoặc |3x+1|=8
\(\Leftrightarrow3x+1\in\left\{8;-8;14;-14\right\}\)
hay \(x\in\left\{\dfrac{7}{3};-3;\dfrac{13}{3};-5\right\}\)
`a)`\(\left|x+\dfrac{1}{5}-4\right|=2\)
\(\Rightarrow\left|x-\dfrac{19}{5}\right|=2\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{19}{5}=2\\x-\dfrac{19}{5}=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{29}{5}\\x=\dfrac{9}{5}\end{matrix}\right.\)
`b)`||3x+1|-11|=3
\(\Rightarrow\left[{}\begin{matrix}\left|3x+1\right|-11=3\\\left|3x+1\right|-11=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left|3x+1\right|=14\left(1\right)\\\left|3x+1\right|=8\left(2\right)\end{matrix}\right.\)
\(\left(1\right)\Rightarrow\left[{}\begin{matrix}3x+1=14\\3x+1=-14\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{13}{3}\\x=-5\end{matrix}\right.\)
\(\left(2\right)\Rightarrow\left[{}\begin{matrix}3x+1=8\\3x+1=-8\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=-3\end{matrix}\right.\)