Answer
$x=\dfrac{16}{15}$
Work Step by Step
Using the properties of equality, the solution to the given equation, $
\dfrac{1}{6}\left( \dfrac{3}{4}x-2 \right)=-\dfrac{1}{5}
$, is
\begin{array}{l}
\dfrac{3}{24}x-\dfrac{2}{6}=-\dfrac{1}{5}
\\\\
\dfrac{1}{8}x-\dfrac{1}{3}=-\dfrac{1}{5}
\\\\
\dfrac{1}{8}x=-\dfrac{1}{5}+\dfrac{1}{3}
\\\\
\dfrac{1}{8}x=-\dfrac{3}{15}+\dfrac{5}{15}
\\\\
\dfrac{1}{8}x=\dfrac{2}{15}
\\\\
8\cdot\dfrac{1}{8}x=\dfrac{2}{15}\cdot8
\\\\
x=\dfrac{16}{15}
.\end{array}
CHECKING:
\begin{array}{l}
\dfrac{1}{6}\left( \dfrac{3}{4}\cdot\dfrac{16}{15}-2 \right)=-\dfrac{1}{5}
\\\\
\dfrac{1}{6}\left( \dfrac{48}{60}-2 \right)=-\dfrac{1}{5}
\\\\
\dfrac{1}{6}\left( \dfrac{4}{5}-2 \right)=-\dfrac{1}{5}
\\\\
\dfrac{1}{6}\left( \dfrac{4}{5}-\dfrac{10}{5} \right)=-\dfrac{1}{5}
\\\\
\dfrac{1}{6}\left( -\dfrac{6}{5} \right)=-\dfrac{1}{5}
\\\\
-\dfrac{1}{5}=-\dfrac{1}{5}
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
x=\dfrac{16}{15}
$.
