#### Answer

$t\le-6$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
\dfrac{2t-9}{-3}\ge7
.$
$\bf{\text{Solution Details:}}$
Multiplying both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2t-9}{-3}\ge7
\\\\
-3\left( \dfrac{2t-9}{-3} \right)\ge-3(7)
\\\\
2t-9\le-21
.\end{array}
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
2t-9\le-21
\\\\
2t\le-21+9
\\\\
2t\le-12
\\\\
t\le-\dfrac{12}{2}
\\\\
t\le-6
.\end{array}