## Intermediate Algebra (12th Edition)

$\left( -6,4 \right)$
$\bf{\text{Solution Outline:}}$ 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 $\left( -6,4 \right) .$