Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 45

$x\gt64$

Multiplying both sides by the $LCD= 30 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{x+2}{6}-\dfrac{x+1}{5}\lt-2 ,$ is \begin{array}{l}\require{cancel} 5(x+2)-6(x+1)\lt30(-2) \\\\ 5x+10-6x-6\lt-60 \\\\ 5x-6x\lt-60-10+6 \\\\ -x\lt-64 \\\\ x\gt64 .\end{array}