\(3\left|4x-1\right|-2=19\)
\(3\left|4x-1\right|=21\)
\(\left|4x-1\right|=7\)
⇔\(\left[{}\begin{matrix}4x-1=7\\4x-1=-7\end{matrix}\right.\)
⇔\(\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\)
\(\Rightarrow\left|4x-1\right|=21:3=7\\ \Rightarrow\left[{}\begin{matrix}4x-1=7\\4x-1=-7\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\)
\(3.\left|4x-1\right|-2=19\)
<=> \(\left[{}\begin{matrix}3.\left(4x-1\right)-2=19\left(x\ge\dfrac{1}{4}\right)\\3.\left[-\left(4x-1\right)\right]-2=19\left(x< \dfrac{1}{4}\right)\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}12x-3-2=19\\3.\left(-4x+1\right)-2=19\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=2\left(TM\right)\\x=-\dfrac{3}{2}\left(TM\right)\end{matrix}\right.\)
\(3\left|4x-1\right|-2=19\)
\(\Leftrightarrow3\left|4x-1\right|=21\)
\(\Leftrightarrow\left|4x-1\right|=7\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-1=7\\4x-1=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\)