Answer
$\text{the interval } (-1,7]$
Work Step by Step
Solving the inequalities separately, then,
\begin{array}{l}
3x+4\gt1\\\\
3x\gt-3\\\\
x\gt-1
,\\\\\text{AND}\\\\
2x-5\le9\\\\
2x\le14\\\\
x\le7
.\end{array}
Using the conjunction "AND", the solution set is the set common to both inequalities. Hence, the solution set is $
\text{the interval } (-1,7]
$.
