## Intermediate Algebra (12th Edition)

$\left( -\infty,-\dfrac{28}{3} \right)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $\dfrac{3x-2}{-5}\gt6 ,$ 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 $\ge.$ For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Multiplying both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to \begin{array}{l}\require{cancel} -5\left( \dfrac{3x-2}{-5} \right) \lt-5(6) \\\\ 3x-2\lt-30 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 3x\lt-30+2 \\\\ 3x\lt-28 \\\\ x\lt-\dfrac{28}{3} .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $\left( -\infty,-\dfrac{28}{3} \right) .$