#### Answer

$\text{Set Builder Notation: }
\{t|t\le -3\}
\\\text{Interval Notation: }
(-\infty,-3]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
5\ge t+8
.$ Write the answer in both set-builder notation and interval notation. Finally, graph the solution set.
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
5\ge t+8
\\\\
-t\ge 8-5
\\\\
-t\ge 3
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-t\ge 3
\\\\
\dfrac{-t}{-1}\ge \dfrac{3}{-1}
\\\\
t\le -3
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\{t|t\le -3\}
\\\text{Interval Notation: }
(-\infty,-3]
.\end{array}