Chapter 6 - Section 6.6 - Rational Equations and Problem Solving - Exercise Set - Page 389: 64

$x=22$

By cross-multiplication and using the properties of equality, the solution to the given equation, $ \dfrac{x-6}{4}=\dfrac{x-2}{5} ,$ is \begin{array}{l} 5(x-6)=4(x-2) \\\\ 5x-30=4x-8 \\\\ 5x-4x=-8+30 \\\\ x=22 .\end{array}