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

$t\ge-\dfrac{13}{3}$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $\dfrac{3t-7}{-4}\le5 .$ $\bf{\text{Solution Details:}}$ Multiplying both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} \dfrac{3t-7}{-4}\le5 \\\\ -4\left( \dfrac{3t-7}{-4} \right)\le-4(5) \\\\ 3t-7\ge-20 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 3t-7\ge-20 \\\\ 3t\ge-20+7 \\\\ 3t\ge-13 \\\\ t\ge-\dfrac{13}{3} .\end{array}