Answer
$\text{Set Builder Notation: }
\left\{ y|y\gt\dfrac{7}{12} \right\}
\\\text{Interval Notation: }
\left( \dfrac{7}{12},\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
y-\dfrac{1}{3}\gt\dfrac{1}{4}
.$ 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-\dfrac{1}{3}\gt\dfrac{1}{4}
\\\\
12\left( y-\dfrac{1}{3} \right)\gt12\left(\dfrac{1}{4}\right)
\\\\
12y-4\gt3
\\\\
12y\gt3+4
\\\\
12y\gt7
\\\\
y\gt\dfrac{7}{12}
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ y|y\gt\dfrac{7}{12} \right\}
\\\text{Interval Notation: }
\left( \dfrac{7}{12},\infty \right)
.\end{array}
