Answer
$\text{Set Builder Notation: }
\left\{ y|y\le-4 \right\}
\\\text{Interval Notation: }
\left( -\infty,-4 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
7-3y\ge27+2y
.$ Write the answer in both set-builder notation and interval notation.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
7-3y\ge27+2y
\\\\
-3y-2y\ge27-7
\\\\
-5y\ge20
.\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}
-5y\ge20
\\\\
y\le\dfrac{20}{-5}
\\\\
y\le-4
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ y|y\le-4 \right\}
\\\text{Interval Notation: }
\left( -\infty,-4 \right]
.\end{array}
