## Intermediate Algebra: Connecting Concepts through Application

$x\ge-1$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $2x+6\le5x+9 ,$ use the properties of inequality to isolate the variable. Then, graph the solution set. In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 2x+6\le5x+9 \\\\ 2x-5x\le9-6 \\\\ -3x\le3 .\end{array} Dividing both sides by a negative number (and consequently reversing the sign) results to \begin{array}{l}\require{cancel} -3x\le3 \\\\ \dfrac{-3x}{-3}\ge\dfrac{3}{-3} \\\\ x\ge-1 .\end{array}