## Elementary Algebra

$x\gt64$
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}