Decide, solve

Decide (решать[, что делать]) и solve (решать[задачу, проблему]) .

Мы говорим solve, когда требуется создание решения, как, например, решение математической задачи: solve a mathematical problem, solve a difficult problem.

 Примеры:

When I came across this paragraph my problem was solved.
Agatha Christie, The Secret Adversary

Tuppence was undecided for the moment whether to put him down as an actor or a lawyer, but her doubts were soon solved as he gave her his name: Sir James Peel Edgerton.
Agatha Christie, The Secret Adversary

Мы говорим decide, когда нужно сделать выбор из уже существующих решений, из имеющихся вариантов: decide what to do.

 Примеры:

"That's all very well," I objected, "but how are you going to decide what is important, and what isn't? That always seems the difficulty to me."
 Agatha Christie, The Mysterious Affair at Styles

So far he had aroused no suspicion. But he must decide quickly on his next step.
Agatha Christie, The Secret Adversary