## Intermediate Algebra (12th Edition)

$(2,3)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $2x+4\lt10 \text{ and } 3x-1\gt5 ,$ solve each inequality separately. Since the conjunction "AND" is used, the solution set is the set of numbers common to 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\lt10 \\\\ 2x\lt10-4 \\\\ 2x\lt6 \\\\ x\lt\dfrac{6}{2} \\\\ x\lt3 \\\\\text{AND}\\\\ 3x-1\gt5 \\\\ 3x\gt5+1 \\\\ 3x\gt6 \\\\ x\gt\dfrac{6}{3} \\\\ x\gt2 .\end{array} Since "AND" is used, then the solution set is the set of numbers common to both inequalities. Hence, the solution set is the interval $(2,3) .$