Chapter 3 - Equations and Problem Solving - 3.1 - Solving First-Degree Equations - Problem Set 3.1 - Page 100: 61

$x=-\dfrac{7}{5}$

Multiplying both sides by the $LCD= 7 ,$ and using the properties of equality, the value of the variable that satisfies the given equation, $ -\dfrac{5}{7}x=1 ,$ is \begin{array}{l}\require{cancel} 1(-5x)=7(1) \\\\ -5x=7 \\\\ x=\dfrac{7}{-5} \\\\ x=-\dfrac{7}{5} .\end{array}