Answer
$\text{Set Builder Notation: }
\left\{ x|x\lt-7 \right\}
\\\text{Interval Notation: }
\left( -\infty,-7 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
3-5x\gt38
.$ 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}
3-5x\gt38
\\\\
-5x\gt38-3
\\\\
-5x\gt35
.\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}
-5x\gt35
\\\\
x\lt\dfrac{35}{-5}
\\\\
x\lt-7
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\lt-7 \right\}
\\\text{Interval Notation: }
\left( -\infty,-7 \right)
.\end{array}
