Answer
$[13,\infty)$
Work Step by Step
$\displaystyle \frac{x-4}{6}\geq\frac{x-2}{9}+\frac{5}{18}\qquad$ ... multiply both sides with the LCD, 18
$ 3(x-4)\geq 2(x-2)+5\qquad$ ... distribute
$ 3x-12\geq 2x-4+5\qquad$ ... add $12-2x $ to both sides
$x\geq 13$
Solution set : $[13,+\infty)$
