Đáp án:
\(\begin{array}{l}
a)\left[ \begin{array}{l}
x = \dfrac{5}{4}\\
x = \dfrac{1}{4}
\end{array} \right.\\
c)\left[ \begin{array}{l}
x = \dfrac{{13}}{{20}}\\
x = \dfrac{7}{{20}}
\end{array} \right.\\
b)\left[ \begin{array}{l}
x = \dfrac{5}{4}\\
x = \dfrac{7}{4}
\end{array} \right.
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left| {2x - \dfrac{3}{2}} \right| = \dfrac{{7 - 3}}{4}\\
\to \left| {2x - \dfrac{3}{2}} \right| = 1\\
\to \left[ \begin{array}{l}
2x - \dfrac{3}{2} = 1\\
2x - \dfrac{3}{2} = - 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{5}{4}\\
x = \dfrac{1}{4}
\end{array} \right.\\
c)\left| {\left| {2x - 1} \right| + \dfrac{1}{2}} \right| = \dfrac{4}{5}\\
\to \left[ \begin{array}{l}
\left| {2x - 1} \right| + \dfrac{1}{2} = \dfrac{4}{5}\\
\left| {2x - 1} \right| + \dfrac{1}{2} = - \dfrac{4}{5}
\end{array} \right.\\
\to \left[ \begin{array}{l}
\left| {2x - 1} \right| = \dfrac{3}{{10}}\\
\left| {2x - 1} \right| = - \dfrac{{13}}{{10}}\left( l \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x - 1 = \dfrac{3}{{10}}\\
2x - 1 = - \dfrac{3}{{10}}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{{13}}{{20}}\\
x = \dfrac{7}{{20}}
\end{array} \right.\\
b)\dfrac{4}{3} - \left| {3 - 2x} \right| = \dfrac{5}{6}\\
\to \left| {3 - 2x} \right| = \dfrac{1}{2}\\
\to \left[ \begin{array}{l}
3 - 2x = \dfrac{1}{2}\\
3 - 2x = - \dfrac{1}{2}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{5}{4}\\
x = \dfrac{7}{4}
\end{array} \right.
\end{array}\)
