Answer
$\text{Set Builder Notation: }
\left\{ t|t\lt3 \right\}
\\\text{Interval Notation: }
\left( -\infty,3 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
8-t\gt5
.$ Write the answer in both set-builder notation and interval notation.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
8-t\gt5
\\\\
-t\gt5-8
\\\\
-t\gt-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\gt-3
\\\\
t\lt\dfrac{-3}{-1}
\\\\
t\lt3
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ t|t\lt3 \right\}
\\\text{Interval Notation: }
\left( -\infty,3 \right)
.\end{array}
