Chapter 3 - Equations and Problem Solving - Chapter 3 Test - Page 139: 9

$x=12$

Multiplying both sides by the $LCD= 12 $ and using the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{x-2}{4}=\dfrac{x+3}{6} ,$ is \begin{array}{l}\require{cancel} 3(x-2)=2(x+3) \\\\ 3x-6=2x+6 \\\\ 3x-2x=6+6 \\\\ x=12 .\end{array}