Answer
$\left[ \dfrac{29}{6},\infty \right)$
Work Step by Step
Using the properties of inequality, the expression $
\dfrac{3-4x}{6}-\dfrac{1-2x}{12}\le-2
$ simplifies to
\begin{array}{l}
12\left( \dfrac{3-4x}{6}-\dfrac{1-2x}{12} \right) \le \left( -2 \right)12\\\\
2(3-4x)-1(1-2x)\le-24\\
6-8x-1+2x\le-24\\
-6x+5\le-24\\
-6x\le-29\\
x\ge\dfrac{29}{6}
.\end{array}
In interval notation, the solution set is $
\left[ \dfrac{29}{6},\infty \right)
$.