Answer
$[-\displaystyle \frac{19}{6},\infty)$
Work Step by Step
$\displaystyle \frac{4x-3}{6}+2\geq\frac{2x-1}{12}\qquad$ ... multiply both sides with the LCD, $12$
$ 2(4x-3)+24\geq 2x-1\qquad$ ... distribute
$ 8x-6+24\geq 2x-1\qquad$ ... add $18-2x $ to both sides
$6x\geq-19\qquad$ ... divide both sides with 6
$x\displaystyle \geq-\frac{19}{6}$
Solution set : $[-\displaystyle \frac{19}{6},+\infty)$
