Answer
$-5\lt w\lt 6$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |2w-1|\lt 11$
Write a compound inequality.
$\Rightarrow 2w-1\lt 11$ and $2w-1\gt -11$
Add $1$ to each side.
$\Rightarrow 2w-1+1\lt 11+1$ and $2w-1+1\gt -11+1$
Simplify.
$\Rightarrow 2w\lt 12$ and $2w\gt -10$
Divide each side by $2$.
$\Rightarrow \frac{2w}{2}\lt \frac{12}{2}$ and $\frac{2w}{2}\gt \frac{-10}{2}$
Simplify.
$\Rightarrow w\lt 6$ and $w\gt -5$
Hence, the solution is $-5\lt w \lt 6$.
