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

$m\le2$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $4m+7\ge9m-3 .$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given inequality is equivalent to \begin{array}{l}\require{cancel} 4m+7\ge9m-3 \\\\ 4m-9m\ge-3-7 \\\\ -5m\ge-10 .\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} -5m\ge-10 \\\\ m\le\dfrac{-10}{-5} \\\\ m\le2 .\end{array}