Intermediate Algebra (12th Edition)

$\left( -2,2 \right)$
$\bf{\text{Solution Outline:}}$ Use the concepts of inequalities to translate the given description, \begin{array}{l}\require{cancel}\text{ 6 times a number is between $-12$ and $12$ },\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} -12 \lt 6x \lt 12 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -\dfrac{12}{6} \lt \dfrac{6x}{6} \lt \dfrac{12}{6} \\\\ -2 \lt x \lt 2 .\end{array} In interval notation, the solution set is $\left( -2,2 \right) .$