Answer
The solution set is $[13, \infty)$
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{x-4}{6}\geq\frac{x-2}{9}+\frac{5}{18}\qquad $ ... $/\times 18$ ... ($\times $ LCD)
$ 3(x-4)\geq 2(x-2)+5\qquad $ ... distribute
$ 3x-12\geq 2x-4+5\qquad $ ... $/-2x+12$
$ x\geq 13$
The solution set is $[13, \infty)$
