Answer
$(-\infty,2)$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$\Rightarrow -2x+5\gt7$ or $-3x+10\gt2x$.
Solve each inequality separately.
$\Rightarrow -2x+5\gt7$ or $-3x+10\gt2x$.
$\Rightarrow 5\gt7+2x$ or $10\gt2x+3x$.
$\Rightarrow 5-7\gt2x$ or $10\gt5x$.
$\Rightarrow -2\gt2x$ or $2\gt x$.
$\Rightarrow -1\gt x$ or $2\gt x$.
First graph then take the union of the solution sets of the two inequalities.
The graph is shown in the image file.
We can write the compound inequality.
$-1\gt x$ as $(-\infty,-1)$ and $2\gt x$ as $(-\infty,2)$
The union is
$(-\infty,-1)\cup(-\infty,2)=(-\infty,2)$.
