Learn Hardcore Russian: Тебе нужно решить задачу до завтра. - You need to solve the problem by tomorrow.

Because with the impersonal modal нужно, Russian marks the person who must act with the dative. There is no nominative “you” here; “тебе” tells us to whom the necessity applies.

What is the role of нужно in this sentence?

нужно is an impersonal predicative meaning “it is necessary” or “one needs to.” It doesn’t conjugate for person or number and always pairs with a dative pronoun plus an infinitive to express obligation or necessity.

Why is there no explicit subject before нужно?

Impersonal constructions in Russian drop the grammatical subject. The sense of “someone must” is carried by the dative pronoun (“тебе”), and нужно itself cannot have a nominative subject.

What case is задачу in, and why is that case used?

задачу is in the accusative singular feminine. It functions as the direct object of the infinitive verb решить (“to solve”), and transitive verbs take their object in the accusative.

Why use решить (perfective) instead of решать (imperfective)?

The perfective решить emphasizes that the action must be completed by the deadline. The imperfective решать would suggest an ongoing or repeated process, not a one‐time completion.

What does до завтра mean and how is it constructed?

до is a preposition meaning “until” or “by,” which normally takes the genitive. Colloquially, завтра (an adverb) stands in for “завтрашнего дня” in the genitive. So до завтра means “by tomorrow.” A more formal phrase is до завтрашнего дня.

Can I replace тебе нужно with тебе надо, and is there a difference?

Yes. надо is a synonym of нужно and also takes a dative plus an infinitive. надо is slightly more colloquial but the meaning (“you need to…”) remains the same.

How else could I express “You must solve the problem by tomorrow” in Russian?

You could say: • Ты должен решить задачу до завтрашнего дня. – using the modal adjective должен which agrees with “ты” (masculine).
• Or colloquially: Надо решить задачу до завтра.