Answer
$r\gt-3$
Work Step by Step
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}
