Answer
$[-\displaystyle \frac{19}{6}, \infty)$
Work Step by Step
The idea is to isolate x on one side.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
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$\displaystyle \frac{4x-3}{6}+2\geq\frac{2x-1}{12}\qquad $ ... $/\times 12$ ... ($\times $ LCD)
$ 2(4x-3)+24\geq 2x-1\qquad $ ... distribute
$8x-6+24\geq 2x-1$
$ 6x+18\geq-1 \qquad $ ... $/-2x+18$
$ 6x\geq-19\qquad $ ... $/\div 6$
$ x\displaystyle \geq-\frac{19}{6}$
The solution set is $[-\displaystyle \frac{19}{6}, \infty)$
