Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 29

$x=-4$

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{x+1}{6}=\dfrac{x+2}{4} ,$ is \begin{array}{l}\require{cancel} 4(x+1)=6(x+2) \\\\ 4x+4=6x+12 \\\\ 4x-6x=12-4 \\\\ -2x=8 \\\\ x=\dfrac{8}{-2} \\\\ x=-4 .\end{array}