Answer
$\text{Set Builder Notation: }
\{ x|x\gt4 \}
\\\text{Interval Notation: }
(4,\infty)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-16x\lt-64
.$ 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 $\ge.$
$\bf{\text{Solution Details:}}$
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-16x\lt-64
\\\\
x\gt\dfrac{-64}{-16}
\\\\
x\gt4
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\{ x|x\gt4 \}
\\\text{Interval Notation: }
(4,\infty)
.\end{array}
