The Noble Eightfold Path is a skillful way of explaining techniques to work on different aspects of our life. We want to get Right View, we want to get Right Speech, we want to get Right Livelihood and so on.
Now the minute we have Right Speech, are we lessening our Dukkha? Yes! The minute we have a Right Livelihood, are we lessening our Dukkha? Yes. Where's Dukkha coming from? As this question states, ignorance and craving. So in order to have right thought, right So if we're able even for one day to lessen or end Dukkha, then there is a cessation of ignorance and craving. You can't end Dukkha without ending the ignorance which is behind it. So the Noble Eightfold Path is basically a way of explaining where we're going to start working in these eight different areas.