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

$\text{Set Builder Notation: } \left\{ t|t\lt3 \right\} \\\text{Interval Notation: } \left( -\infty,3 \right)$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $8-t\gt5 .$ 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} 8-t\gt5 \\\\ -t\gt5-8 \\\\ -t\gt-3 .\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} -t\gt-3 \\\\ t\lt\dfrac{-3}{-1} \\\\ t\lt3 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ t|t\lt3 \right\} \\\text{Interval Notation: } \left( -\infty,3 \right) .\end{array}