#### Answer

$x\gt-\dfrac{3}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given, $
-6x-5\lt4
.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
-6x-5\lt4
\\\\
-6x\lt4+5
\\\\
-6x\lt9
.\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}
-6x\lt9
\\\\
x\gt\dfrac{9}{-6}
\\\\
x\gt-\dfrac{3}{2}
.\end{array}