Answer
$(-\infty,-3)\cup(5,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow -4\left | 1-x\right |\lt-16$
Divide both sides by $4$.
$\Rightarrow \frac{-4\left | 1-x\right |}{4}\lt\frac{-16}{4}$
Simplify.
$\Rightarrow -\left | 1-x\right |\lt-4$
Multiply all parts by −1 and change the sense of the inequality.
$\Rightarrow -1(-\left | 1-x\right |)\gt-1(-4)$
Simplify.
$\Rightarrow \left | 1-x\right |\gt4$
Rewrite the inequality without absolute value bars.
$\Rightarrow 1-x\lt-4$ or $1-x\gt4$
Solve each inequality separately.
Subtract $1$ from all sides.
$\Rightarrow 1-x-1\lt-4-1$ or $1-x-1\gt4-1$
Simplify.
$\Rightarrow -x\lt-5$ or $-x\gt3$
Multiply all parts by −1 and change the sense of the inequality.
$\Rightarrow -1(-x)\gt-1(-5)$ or $-1(-x)\lt-1(3)$
Simplify.
$\Rightarrow x\gt5$ or $x\lt-3$
The solution set is less than $-3$ or greater than $5$.
The interval notation is
$(-\infty,-3)\cup(5,\infty)$.
