Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$r\gt-3$
Remember that when we divide or multiply an inequality by a negative, we have to flip the sign of the inequality. Using the Distributive Property and the properties of inequality, the solution to the given inequality, $3(r-6)+2\lt4(r+2)-21 ,$ is \begin{array}{l}\require{cancel} 3(r)+3(-6)+2\lt4(r)+4(2)-21 \\\\ 3r-18+2\lt4r+8-21 \\\\ 3r-16\lt4r-13 \\\\ 3r-4r\lt-13+16 \\\\ -r\lt3 \\\\ r\gt-3 .\end{array}