#### Answer

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

#### Work Step by Step

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}