Đáp án:
\(\left[ \begin{array}{l}
x = \dfrac{3}{{11}}\\
x = \dfrac{1}{5}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left| {4x - 1} \right| - \left| {\dfrac{{3x - 1}}{2}} \right| = 0\\
\to \left| {4x - 1} \right| = \left| {\dfrac{{3x - 1}}{2}} \right|\\
\to \left[ \begin{array}{l}
4x - 1 = \dfrac{{3x - 1}}{2}\left( {DK:x \ge \dfrac{1}{3}} \right)\\
4x - 1 = - \dfrac{{3x - 1}}{2}\left( {DK:\dfrac{1}{3} > x \ge \dfrac{1}{4}} \right)\\
- 4x + 1 = - \dfrac{{3x - 1}}{2}\left( {DK:x < \dfrac{1}{4}} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
8x - 2 = 3x - 1\\
8x - 2 = - 3x + 1\\
- 8x + 2 = - 3x + 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
5x = 1\\
11x = 3\\
5x = 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{3}{{11}}\\
x = \dfrac{1}{5}
\end{array} \right.
\end{array}\)
