Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 38

$x=\dfrac{2}{5}$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{3}{x-10}=\dfrac{-2}{x+6} ,$ is \begin{array}{l}\require{cancel} 3(x+6)=-2(x-10) \\\\ 3x+18=-2x+20 \\\\ 3x+2x=20-18 \\\\ 5x=2 \\\\ x=\dfrac{2}{5} .\end{array}