Tienen que adaptar el presupuesto, pese a que solucionaron el problema.

Questions & Answers about Tienen que adaptar el presupuesto, pese a que solucionaron el problema.

Why is solucionaron in the indicative rather than the subjunctive here?
In concessive clauses (phrases that introduce an obstacle, like "even though"), we use the indicative when the obstacle is a declared, known fact. Because they actually did solve the problem, solucionaron is in the indicative. If the obstacle were hypothetical or in the future, we would use the subjunctive.
How would the sentence change if we wanted to say "even if they solve the problem"?
To express a hypothetical or future obstacle ("even if they solve it"), you must use the subjunctive. The second half of the sentence would become pese a que solucionen el problema.
Is there a difference in meaning between pese a que and a pesar de que?
No, they both mean "even though" or "despite the fact that" and are generally interchangeable. Pese a que can sometimes feel slightly more formal, but you could easily say a pesar de que solucionaron el problema here with no change in meaning.
Since the subject "they" is the same for both verbs, could we drop the que and use an infinitive?
Yes! Just like with antes de or después de, when the subject performing both actions is exactly the same, you can drop the que and use the infinitive. You could rewrite the second half as pese a solucionar el problema.

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