Learn Dutch: Zonder het ventiel werkt de fietspomp niet. - The bicycle pump does not work without the valve.

Because the prepositional phrase Zonder het ventiel is placed at the beginning of the sentence for emphasis. In Dutch, whenever something other than the subject occupies the first position, the verb and subject swap places to keep the conjugated verb in the second position.

Since this lesson is about fronting verbs for contrast, how would we rewrite this sentence to put the focus on the verb werkt?

You would move the infinitive Werken to the front and use the dummy verb doen (to do) as your conjugated verb. The sentence becomes: Werken doet de fietspomp niet zonder het ventiel. This emphasizes the action itself, contrasting it with something else (e.g., maybe it looks nice, but it doesn't work).

Why is niet placed at the very end of the sentence here?

When niet negates the entire sentence or the action of the main verb itself (in this case, the fact that the pump works), it is pushed to the very end of the clause.

How do we know which definite article to use for ventiel and fietspomp?

Ventiel is simply a neuter noun, so it takes het. For fietspomp, the gender is determined by the final part of the compound word, which is pomp. Because it is de pomp, the entire compound word automatically takes de.