## Intermediate Algebra (6th Edition)

$\left( \dfrac{1}{6},\dfrac{7}{2} \right)$
Using the properties of inequality, the solution set of the given inequality, $\dfrac{2}{3}\lt x+\dfrac{1}{2}\lt4 ,$ is \begin{array}{l}\require{cancel} \dfrac{2}{3}-\dfrac{1}{2}\lt x+\dfrac{1}{2}-\dfrac{1}{2}\lt4-\dfrac{1}{2} \\\\ \dfrac{4}{6}-\dfrac{3}{6}\lt x\lt\dfrac{8}{2}-\dfrac{1}{2} \\\\ \dfrac{1}{6}\lt x\lt\dfrac{7}{2} .\end{array} Hence, the solution set is $\left( \dfrac{1}{6},\dfrac{7}{2} \right) .$