Answer
$v=1$ or $v=3$
Work Step by Step
Using the definition of the absolute value, we have
\begin{align*}
|2-v|&=-1
\\&\Longrightarrow 2-v=-1 \quad \text{or} \quad 2-v=1
\\&\Longrightarrow -v=-1-2\quad \text{or} \quad -v=1-2
\\&\Longrightarrow -v=-3\quad \text{or} \quad -v=-1
\\&\Longrightarrow v=3\quad \text{or} \quad v=1
\end{align*}
Thus, we have:
$v=3$ or $v=1$
