Intermediate Algebra (12th Edition)

$\left( -9,\infty \right)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-\dfrac{2}{3}x \lt 6 ,$ 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} 3\left( -\dfrac{2}{3}x \right)\lt 3(6) \\\\ -2x\lt 18 .\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\gt \dfrac{18}{-2} \\\\ x\gt -9 .\end{array} In interval notation, the solution set is $\left( -9,\infty \right) .$