#### Answer

$\text{Set Builder Notation: }
\left\{ n|n\lt-5 \right\}
\\\text{Interval Notation: }
\left( -\infty,-5 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
4n+3\lt-17
.$ 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}
4n+3\lt-17
\\\\
4n\lt-17-3
\\\\
4n\lt-20
\\\\
n\lt-\dfrac{20}{4}
\\\\
n\lt-5
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ n|n\lt-5 \right\}
\\\text{Interval Notation: }
\left( -\infty,-5 \right)
.\end{array}