Answer
$\text{Set Builder Notation: }
\left\{ y|y\le-13 \right\}
\\\text{Interval Notation: }
\left( -\infty,-13 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-5y\ge65
.$ 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}
-5y\ge65
\\\\
y\le\dfrac{65}{-5}
\\\\
y\le-13
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ y|y\le-13 \right\}
\\\text{Interval Notation: }
\left( -\infty,-13 \right]
.\end{array}
