## Intermediate Algebra (12th Edition)

$(-\infty,2)\cup(3,\infty)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $2x+4\gt10 \text{ or } 3x-1\lt5 ,$ solve each inequality separately. Since the conjunction "OR" is used, the solution set is the combined solution sets of both inequalities. $\bf{\text{Solution Details:}}$ Using the properties of inequality to solve each inequality separately results to \begin{array}{l}\require{cancel} 2x+4\gt10 \\\\ 2x\gt10-4 \\\\ 2x\gt6 \\\\ x\gt\dfrac{6}{2} \\\\ x\gt3 \\\\\text{ or }\\\\ 3x-1\lt5 \\\\ 3x\lt5+1 \\\\ 3x\lt6 \\\\ x\lt\dfrac{6}{3} \\\\ x\lt2 .\end{array} Since "OR" is used, then the solution set is the combined solution sets of both inequalities. Hence, the solution set is the interval $(-\infty,2)\cup(3,\infty) .$