#### Answer

$\left( -\infty,1 \right]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-5x-4\ge3(2x-5)
,$ use the Distributive Property and the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-5x-4\ge3(2x)+3(-5)
\\\\
-5x-4\ge6x-15
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-5x-6x\ge-15+4
\\\\
-11x\ge-11
.\end{array}
Dividing both sides by a negative number and consequently reversing the inequality symbol results to
\begin{array}{l}\require{cancel}
\dfrac{-11x}{-11}\le\dfrac{-11}{-11}
\\\\
x\le1
.\end{array}
Hence, the solution set is the interval $
\left( -\infty,1 \right]
.$