#### Answer

$-\dfrac{3}{2}\lt x\le\dfrac{1}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}