Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 183: 8

$x=4$

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}