Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 33

$x=-28$

Multiplying both sides by the $LCD= 6 ,$ the value of the variable that satisfies the given equation, $ \dfrac{x+1}{3}-\dfrac{x+2}{2}=4 ,$ is \begin{array}{l}\require{cancel} 2(x+1)-3(x+2)=6(4) \\\\ 2x+2-3x-6=24 \\\\ 2x-3x=24-2+6 \\\\ -x=28 \\\\ x=-28 .\end{array}