## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=-1$
$\bf{\text{Solution Outline:}}$ 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 $x=-1 .$