## Intermediate Algebra (12th Edition)

$\left( \infty,-3 \right]$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-5x-4\ge11 ,$ use the properties of inequality. For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -5x\ge11+4 \\\\ -5x\ge15 .\end{array} Dividing all sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to \begin{array}{l}\require{cancel} x\le\dfrac{15}{-5} \\\\ x\le-3 .\end{array} In interval notation, the solution set is $\left( \infty,-3 \right] .$