Answer
$x\displaystyle \in(-\frac{1}{2},3]$
Work Step by Step
$\left|x\right|\leq 3\quad \Leftrightarrow\quad x\in[-3,3]$
(property 8 from the table 'Absolute Values and Intervals")
At the same time, $x\displaystyle \gt -1/2 \quad \Leftrightarrow\quad x\in(-\frac{1}{2},\infty]$
So, x is in the intersection of these intervals (see image)
$x\displaystyle \in(-\frac{1}{2},3]$
