## College Algebra (11th Edition)

$\left( -\dfrac{7}{13}, \infty \right)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-9x+3\lt4x+10 ,$ use the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -9x-4x\lt10-3 \\\\ -13x\lt7 .\end{array} Dividing both sides by a negative number and consequently reversing the sign, the inequality above is equivalent to \begin{array}{l}\require{cancel} \dfrac{-13x}{-13}\gt\dfrac{7}{-13} \\\\ x\gt-\dfrac{7}{13} .\end{array} Hence, the solution set is the interval $\left( -\dfrac{7}{13}, \infty \right) .$