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"real world problem" is correct and can be used in written English.
You can use it when referring to any problem that someone might encounter in everyday life. For example: "With increasing air pollution in urban areas, respiratory illnesses have become a real world problem for many people."
Exact(18)
This is, after all, a real world problem.
Our program is distinctive in its unparalleled opportunities for real world problem solving.
The algorithm has also been successfully applied to a real world problem of financial portfolio management.
(5) Finally, the performance of MultiEA is investigated on a real world problem.
To explore the viability of the proposed model, computational experiments are performed on a real world problem.
Flexibility of this MF in applying to real world problem has also been validated through a detailed analysis.
Similar(42)
AHEAD supports real world problem-solving at the interface of wildlife health, livestock health, and human health and livelihoods.
"And so here's a real-world problem.
Engineers are today's real-world problem solvers.
What real-world problem does this solve?
It's great preparation for real-world problem solving because it is real-world problem solving.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com