Answer
$x=\dfrac{8}{3} \quad\text{ or } \quad x=-\dfrac{4}{3} $
Work Step by Step
Using the definition of the absolute value, we have
\begin{align*}
\left|\frac{x}{2}-\frac{1}{3}\right|&=1
\\&\Longrightarrow \frac{x}{2}-\frac{1}{3}=1 \quad\text{or} \quad \frac{x}{2}-\frac{1}{3}=-1
\\&\Longrightarrow \frac{x}{2}=1+\frac{1}{3} \quad \text{or} \quad \frac{x}{2}=-1+\frac{1}{3}
\\&\Longrightarrow \frac{x}{2}=\frac{4}{3} \quad \text{or} \quad \frac{x}{2}=-\frac{2}{3}
\\&\Longrightarrow x=2\cdot\frac{4}{3} \quad \text{or} \quad x=2\cdot \left(-\frac{2}{3}\right)
\\&\Longrightarrow x=\frac{8}{3} \quad \text{or} \quad x=-\frac{4}{3}
\end{align*}
Thus, $x=\dfrac{8}{3}$ or $x=-\dfrac{4}{3} $.
