Answer
$w \geq 8$ or $w \leq 5$
Work Step by Step
Given \begin{equation}
\begin{aligned}
|2 w-13| \geq 3.
\end{aligned}
\end{equation} This an absolute value inequality. The solution is two fold. Solve each of the following inequalities. \begin{equation}
\begin{aligned}
2 w-13&\geq 3\\
2w &\geq 3+13\\
w&\geq \frac{16}{2}\\
w&\geq8\\
\textbf{or}\\
2 w-13&\leq- 3\\
2w &\leq -3+13\\
w&\leq \frac{10}{2}\\
w&\leq 5.
\end{aligned}
\end{equation} Check
\begin{equation}
\begin{aligned}
|2 \cdot 8-13| &\stackrel{?}{\geq }3\\
|3|&= 3\ \checkmark\\
|2 \cdot 5-13| &\stackrel{?}{\geq }3\\
|-3|&= 3\ \checkmark.
\end{aligned}
\end{equation} The solution is $w \geq 8$ or $w \leq 5$.
