Answer
not a solution
Work Step by Step
Substituting $x=
\dfrac{5}{8}
$ in the given equation, $
\dfrac{1}{5}(x+2)=\dfrac{1}{2}\left(x-\dfrac{1}{5}\right)
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{1}{5}\left(\dfrac{5}{8}+2\right)=\dfrac{1}{2}\left(\dfrac{5}{8}-\dfrac{1}{5}\right)
\\\\
\dfrac{1}{5}\left(\dfrac{5}{8}+2\cdot\dfrac{8}{8}\right)=\dfrac{1}{2}\left(\dfrac{5}{8}\cdot\dfrac{5}{5}-\dfrac{1}{5}\cdot\dfrac{8}{8}\right)
\Rightarrow\text{ (change to similar fractions)}
\\\\
\dfrac{1}{5}\left(\dfrac{5}{8}+\dfrac{16}{8}\right)=\dfrac{1}{2}\left(\dfrac{25}{40}-\dfrac{8}{40}\right)
\\\\
\dfrac{1}{5}\left(\dfrac{21}{8}\right)=\dfrac{1}{2}\left(\dfrac{17}{40}\right)
\\\\
\dfrac{21}{40}=\dfrac{17}{80}
\text{ (FALSE)}
.\end{array}
Since the substitution above ended with a FALSE statement, then $
x=\dfrac{5}{8}
,$ is not a solution.
