#### Answer

$\left( -6,4 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the concepts of inequalities to translate the given description,
\begin{array}{l}\require{cancel}\text{
half a number is between $-3$ and $2$
},\end{array}
into symbols. Then solve using the properties of inequality. Express the solution set in interval notation.
$\bf{\text{Solution Details:}}$
In symbols, the given description translates to
\begin{array}{l}\require{cancel}
-3 \lt \dfrac{1}{2}x \lt 2
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
2(-3) \lt 2\left(\dfrac{1}{2}x\right) \lt 2(2)
\\\\
-6 \lt x \lt 4
.\end{array}
In interval notation, the solution set is $
\left( -6,4 \right)
.$