Answer
$(-\infty,2)\cup(8,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow -2\left | 5-x\right |\lt-6$
Divide both sides by $2$.
$\Rightarrow \frac{-2\left | 5-x\right |}{2}\lt\frac{-6}{2}$
Simplify.
$\Rightarrow -\left | 5-x\right |\lt-3$
Multiply all parts by −1 and change the sense of the inequality.
$\Rightarrow -1(-\left | 5-x\right |)\gt-1(-3)$
Simplify.
$\Rightarrow \left | 5-x\right |\gt3$
Rewrite the inequality without absolute value bars.
$\Rightarrow 5-x\lt-3$ or $5-x\gt3$
Solve each inequality separately.
Subtract $5$ from all sides.
$\Rightarrow 5-x-5\lt-3-5$ or $5-x-5\gt3-5$
Simplify.
$\Rightarrow -x\lt-8$ or $-x\gt-2$
Multiply all parts by −1 and change the sense of the inequality.
$\Rightarrow -1(-x)\gt-1(-8)$ or $-1(-x)\lt-1(-2)$
Simplify.
$\Rightarrow x\gt8$ or $x\lt2$
The solution set is less than $2$ or greater than $8$.
The interval notation is
$(-\infty,2)\cup(8,\infty)$.
