Answer
$x\le\dfrac{9}{16}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the properties of inequality to solve the given, $
-2(3x-1)-5\ge6x-4(3-x)
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
-2(3x-1)-5\ge6x-4(3-x)
\\\\
-2(3x)-2(-1)-5\ge6x-4(3)-4(-x)
\\\\
-6x+2-5\ge6x-12+4x
.\end{array}
Using the properties of equality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-6x+2-5\ge6x-12+4x
\\\\
-6x-6x-4x\ge-12-2+5
\\\\
-16x\ge-9
.\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}
-16x\ge-9
\\\\
x\le\dfrac{-9}{-16}
\\\\
x\le\dfrac{9}{16}
.\end{array}
