Đáp án:
$\begin{array}{l}
a)x - \dfrac{1}{2} = 3\dfrac{1}{2}\\
\Rightarrow x = \dfrac{1}{2} + 3\dfrac{1}{2}\\
\Rightarrow x = 4\dfrac{1}{2}\\
\Rightarrow x = \dfrac{9}{2}\\
Vậy\,x = \dfrac{9}{2}\\
b){\left( {3x - \dfrac{1}{2}} \right)^3} = \dfrac{8}{{27}}\\
\Rightarrow {\left( {3x - \dfrac{1}{2}} \right)^3} = {\left( {\dfrac{2}{3}} \right)^3}\\
\Rightarrow 3x - \dfrac{1}{2} = \dfrac{2}{3}\\
\Rightarrow 3x = \dfrac{2}{3} + \dfrac{1}{2}\\
\Rightarrow 3x = \dfrac{7}{6}\\
\Rightarrow x = \dfrac{7}{{18}}\\
Vậy\,x = \dfrac{7}{{18}}\\
c){\left( {\dfrac{1}{3}x - \dfrac{1}{2}} \right)^2} = \dfrac{{25}}{4}\\
\Rightarrow {\left( {\dfrac{1}{3}x - \dfrac{1}{2}} \right)^2} = {\left( {\dfrac{5}{2}} \right)^2} = \left( { - \dfrac{5}{2}} \right)\\
\Rightarrow \left[ \begin{array}{l}
\dfrac{1}{3}x - \dfrac{1}{2} = \dfrac{5}{2}\\
\dfrac{1}{3}x - \dfrac{1}{2} = - \dfrac{5}{2}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
\dfrac{1}{3}x = 3\\
\dfrac{1}{3}x = - 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 9\\
x = - 6
\end{array} \right.\\
Vậy\,x = - 6;x = 9\\
II)a)m = \dfrac{1}{5};n = 10\\
\Rightarrow m = \dfrac{n}{k}\\
\Rightarrow \dfrac{1}{5} = \dfrac{{10}}{k}\\
\Rightarrow k = 50\\
\Rightarrow m = \dfrac{n}{{50}}\\
b)m = \dfrac{2}{3}\\
\Rightarrow n = 50.m = 50.\dfrac{2}{3} = \dfrac{{100}}{3}\\
c)n = 4\\
\Rightarrow m = \dfrac{n}{{50}} = \dfrac{4}{{50}} = \dfrac{2}{{25}}
\end{array}$
