Answer
The solution set is $(-\displaystyle \infty,-\frac{53}{6} ]$
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).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
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$ 18x+45 \leq 12x-8\qquad $ ... $/-45-12x $
$ 6x \leq -53\qquad $ ... $/\div 6$ (positive)
$ x \displaystyle \leq -\frac{53}{6}$
The solution set is $(-\displaystyle \infty,-\frac{53}{6} ]$
