Answer
$-\dfrac{5}{4}\lt x \lt \dfrac{5}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given, $
-15\lt -4x-5\lt0
.$ 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 equality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-15\lt -4x-5\lt0
\\\\
-15+5\lt -4x-5+5\lt0+5
\\\\
-10\lt -4x \lt 5
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-10}{-4}\lt \dfrac{-4x}{-4} \lt \dfrac{5}{-4}
\\\\
\dfrac{5}{2}\gt x \gt -\dfrac{5}{4}
\\\\
-\dfrac{5}{4}\lt x \lt \dfrac{5}{2}
.\end{array}
