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

$y\le-\dfrac{3}{2}$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $3-8y\ge9-4y .$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 3-8y\ge9-4y \\\\ -8y+4y\ge9-3 \\\\ -4y\ge6 .\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} -4y\ge6 \\\\ y\le\dfrac{6}{-4} \\\\ y\le-\dfrac{3}{2} .\end{array}