Đáp án:
b) \(x = \dfrac{5}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left| {\dfrac{1}{4}x - \dfrac{2}{3}} \right| > \dfrac{1}{3}\\
\to \left[ \begin{array}{l}
\dfrac{1}{4}x - \dfrac{2}{3} > \dfrac{1}{3}\left( {DK:x \ge \dfrac{8}{3}} \right)\\
\dfrac{1}{4}x - \dfrac{2}{3} < - \dfrac{1}{3}\left( {DK:x < \dfrac{8}{3}} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
\dfrac{1}{4}x > 1\\
\dfrac{1}{4}x < \dfrac{1}{3}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x > 4\\
x < \dfrac{4}{3}
\end{array} \right.\\
b)\left| {2x - 1} \right| + \left| {2x - 5} \right| = 4\\
\to \left[ \begin{array}{l}
2x - 1 + 2x - 5 = 4\left( {DK:x \ge \dfrac{5}{2}} \right)\\
2x - 1 - 2x + 5 = 4\left( {DK:\dfrac{5}{2} > x \ge \dfrac{1}{2}} \right)\\
- 2x + 1 - 2x + 5 = 4\left( {DK:\dfrac{1}{2} > x} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
4x = 10\\
4 = 4\left( {ld} \right)\\
- 4x = - 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{5}{2}\\
x = \dfrac{1}{2}\left( l \right)
\end{array} \right.
\end{array}\)
