Chapter 3 - Equations and Problem Solving - 3.1 - Solving First-Degree Equations - Problem Set 3.1 - Page 100: 58

$x=\dfrac{25}{42}$

Multiplying both sides by the $LCD= 70 ,$ and using the properties of equality, the value of the variable that satisfies the given equation, $ -\dfrac{6}{5}x=-\dfrac{10}{14} ,$ is \begin{array}{l}\require{cancel} 14(-6x)=5(-10) \\\\ -84x=-50 \\\\ x=\dfrac{-50}{-84} \\\\ x=\dfrac{\cancel{-2}\cdot25}{\cancel{-2}\cdot42} \\\\ x=\dfrac{25}{42} .\end{array}