#### Answer

$x\le-\dfrac{23}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
8x-3(3x+2)-5\ge3(x+4)-2x
,$ 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}
8x-3(3x+2)-5\ge3(x+4)-2x
\\\\
8x-3(3x)-3(2)-5\ge3(x)+3(4)-2x
\\\\
8x-9x-6-5\ge3x+12-2x
.\end{array}
Using the properties of inequality to isolate the variable, then
\begin{array}{l}\require{cancel}
8x-9x-6-5\ge3x+12-2x
\\\\
8x-9x-3x+2x\ge12+6+5
\\\\
-2x\ge23
.\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}
-2x\ge23
\\\\
x\le\dfrac{23}{-2}
\\\\
x\le-\dfrac{23}{2}
.\end{array}