Answer
$\text{Set Builder Notation: }
\{t|t\gt -5\}
\\\text{Interval Notation: }
(-5,\infty)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
4\lt t+9
.$ 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 equation is equivalent to
\begin{array}{l}\require{cancel}
4\lt t+9
\\\\
-t\lt 9-4
\\\\
-t\lt 5
.\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\lt 5
\\\\
\dfrac{-t}{-1}\lt \dfrac{5}{-1}
\\\\
t\gt -5
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\{t|t\gt -5\}
\\\text{Interval Notation: }
(-5,\infty)
.\end{array}