#### Answer

$x\le-\dfrac{5}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the properties of inequality to solve the given, $
-2(x-5)\ge6(x+7)-12
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2(x-5)\ge6(x+7)-12
\\\\
-2(x)-2(-5)\ge6(x)+6(7)-12
\\\\
-2x+10\ge6x+42-12
.\end{array}
Using the properties of equality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2x+10\ge6x+42-12
\\\\
-2x-6x\ge42-12-10
\\\\
-8x\ge20
.\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}
-8x\ge20
\\\\
x\le\dfrac{20}{-8}
\\\\
x\le-\dfrac{5}{2}
.\end{array}