Answer
$(2,5)$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$2x\gt5x-15$ and $7x\gt2x+10$.
Solve each inequality separately.
$\Rightarrow 2x\gt5x-15$ and $7x\gt2x+10$.
$\Rightarrow 2x+15\gt5x$ and $7x-2x\gt10$.
$\Rightarrow 15\gt5x-2x$ and $5x\gt10$.
$\Rightarrow 15\gt3x$ and $5x\gt10$.
$\Rightarrow 5\gt x$ and $x\gt2$.
First graph then take the intersection of the solution sets of the two inequalities.
The graph is shown in the image file.
We can write the compound inequality.
$5\gt x$ as $(-\infty,5)$ and $x\gt2$ as $(2,\infty)$
The intersection is
$(-\infty,5)\cap(2,\infty)=(2,5)$.
