#### Answer

$t\ge-\dfrac{13}{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
\dfrac{3t-7}{-4}\le5
.$
$\bf{\text{Solution Details:}}$
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{3t-7}{-4}\le5
\\\\
-4\left( \dfrac{3t-7}{-4} \right)\le-4(5)
\\\\
3t-7\ge-20
.\end{array}
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
3t-7\ge-20
\\\\
3t\ge-20+7
\\\\
3t\ge-13
\\\\
t\ge-\dfrac{13}{3}
.\end{array}