#### Answer

$x=-1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of equality to solve the given equation, $
\dfrac{5x}{7}=-\dfrac{10}{14}
.$ Then do checking of the solution.
$\bf{\text{Solution Details:}}$
Using the Multiplication Property of Equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5x}{7}=-\dfrac{10}{14}
\\\\
\dfrac{7}{5}\left( \dfrac{5x}{7} \right)=\dfrac{7}{5}\left( -\dfrac{10}{14} \right)
\\\\
x=-\dfrac{70}{70}
\\\\
x=-1
.\end{array}
Substituting the solved value of the variable in the given equation results to
\begin{array}{l}\require{cancel}
\dfrac{5x}{7}=-\dfrac{10}{14}
\\\\
\dfrac{5(-1)}{7}=-\dfrac{10}{14}
\\\\
-\dfrac{5}{7}=-\dfrac{\cancel2(5)}{\cancel2(7)}
\\\\
-\dfrac{5}{7}=-\dfrac{5}{7}
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
x=-1
.$