Answer
$2\lt u$ or $-1\gt u$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow -3|2-4u|+5\lt-13$
Subtract $5$ from each side.
$\Rightarrow -3|2-4u|+5-5\lt-13-5$
Simplify.
$\Rightarrow -3|2-4u|\lt-18$
Divide each side by $-3$. Reverse the inequality symbol.
$\Rightarrow \frac{-3|2-4u|}{-3}\gt\frac{-18}{-3}$
Simplify.
$\Rightarrow |2-4u|\gt6$
Write a compound inequality.
$\Rightarrow 2-4u\lt -6$ or $2-4u\gt 6$
Add $4u+6$ to each side of the first inequality and $4u-6$ to each side of the second inequality.
$\Rightarrow 2-4u+4u+6\lt -6+4u+6$ or $2-4u+4u-6\gt 6+4u-6$
Simplify.
$\Rightarrow 8\lt 4u$ or $-4\gt 4u$
Divide each side by $4$.
$\Rightarrow \frac{8}{4}\lt \frac{4u}{4}$ or $\frac{-4}{4}\gt \frac{4u}{4}$
Simplify.
$\Rightarrow 2\lt u$ or $-1\gt u$
Hence, the solution is $2\lt u$ or $-1\gt u$.
