#### Answer

$x=4$

#### Work Step by Step

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $
\dfrac{x+2}{12}=\dfrac{x+1}{10}
,$ is
\begin{array}{l}\require{cancel}
10(x+2)=12(x+1)
\\\\
10x+20=12x+12
\\\\
10x-12x=12-20
\\\\
-2x=-8
\\\\
x=\dfrac{-8}{-2}
\\\\
x=4
.\end{array}