Answer
$(6,8)$.
The solution set graph is shown below.
Work Step by Step
The given compound inequality is
$\Rightarrow -2x\lt-12$ and $x-3\lt5$.
First
$\Rightarrow -2x\lt-12$
Divide both sides by $-2$ and change the sense of the inequality..
$\Rightarrow \frac{-2x}{-2}\lt\frac{-12}{-2}$
Simplify.
$\Rightarrow x\gt6$
Second
$\Rightarrow x-3\lt5$
Add $3$ to both sides.
$\Rightarrow x-3+3\lt5+3$
Simplify.
$\Rightarrow x\lt8$
First graph then take the intersection of the solution sets of the two inequalities.
We can write the compound inequality.
$x\lt 8$ as $(-\infty,8)$ and $x\gt 6$ as $(6,\infty)$
The union is
$(-\infty,8)\cup(6,\infty)=(6,8)$.
The graph is shown below.
