Answer
$\text{Set Builder Notation: }
\{ n|n\lt0 \}
\\\text{Interval Notation: }
(-\infty,0)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-8n+12\gt12-7n
.$ 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}
-8n+12\gt12-7n
\\\\
-8n+7n\gt12-12
\\\\
-n\gt0
.\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}
-n\gt0
\\\\
\dfrac{-n}{-1}\gt\dfrac{0}{-1}
\\\\
n\lt0
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\{ n|n\lt0 \}
\\\text{Interval Notation: }
(-\infty,0)
.\end{array}
