Answer
$(2,3)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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)
.$
