Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

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