INTERPRETATION 1
6-(5/9)x≥8,
6-8≥(5/9)x,
-2≥(5/9)x,
-18≥5x,
5x≤-18,
x≤-18/5, that is, x≤-3.6.
INTERPRETATION 2
1/x≤-18/5, that is, 0≤-18/5-1/x.
If x>0, 1≤-18x/5, 5≤-18x, add 18x to each side: 18x+5≤0, 18x≤-5, x≤-5/18. But this makes x negative, not positive as assumed. So we reject this answer. This means x<0.
Inverting a fraction turns the inequality around: x≥-5/18. (If a=2, then a>1; 1/a<1, so the inequality is reversed when the fraction is inverted.) Therefore, -5/18≤x<0.