#### Answer

$\text{Set Builder Notation: }
\{y|y\gt3\}
\\\text{Interval Notation: }
(3,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
y+6\gt9
.$ 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}
y+6\gt9
\\\\
y\gt9-6
\\\\
y\gt3
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\{y|y\gt3\}
\\\text{Interval Notation: }
(3,\infty)
.\end{array}