Answer
$\text{Set Builder Notation: }
\left\{ y|y\gt-7 \right\}
\\\text{Interval Notation: }
\left( -7,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-4y\lt28
.$ Write the answer in both set-builder notation and interval notation.
$\bf{\text{Solution Details:}}$
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-4y\lt28
\\\\
y\gt\dfrac{28}{-4}
\\\\
y\gt-7
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ y|y\gt-7 \right\}
\\\text{Interval Notation: }
\left( -7,\infty \right)
.\end{array}
