Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-\dfrac{3}{2}\lt x\le\dfrac{1}{2}$
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given, $-5\lt4x+1\le3 .$ Then graph the solution set. In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -5\lt4x+1\le3 \\\\ -5-1\lt4x+1-1\le3-1 \\\\ -6\lt4x\le2 \\\\ -\dfrac{6}{4}\lt \dfrac{4x}{4}\le\dfrac{2}{4} \\\\ -\dfrac{3}{2}\lt x\le\dfrac{1}{2} .\end{array}