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"to illustrate this problem" is grammatically correct and commonly used in written English
It is often used when explaining or providing examples to support a particular issue or challenge. Example: "To illustrate this problem, let's examine a real-life scenario. Imagine you are a small business owner struggling to keep up with rising production costs..."
Exact(19)
Two extreme positions serve to illustrate this problem.
To illustrate this problem, one may imagine a person (call her Laura) suffering from the effects of global warming in 2100 and lamenting that radical mitigation policies were not pursued by previous generations.
A security expert named Kenn White was able to illustrate this problem by creating a website that establishes a connection to a website that appears to be a secure link to the Bank of America page, but is in fact a bogus site of his own creation (featuring a criminal Doge in a ski mask).
To illustrate this problem, I made some calculations.
Four subsections will be given to illustrate this problem.
To illustrate this problem, we use the example of detecting buried landmines using GPR sensors1.
Similar(40)
My DP, right now, would like to include a photo to illustrate this grave problem: the one of our ocean filled with plastic bags, garbage and other non-biodegradable debris.
For that purpose we rely on a specific problem borrowed from the OSAl community to illustrate this discussion where the problem of decision making in the context of sensing errors is clearly formalized and the impact of such errors on the considered learning algorithm's performance is quantified.
To illustrate this relation between architectural problems and agglomerations, consider the webgrid component depicted in Fig. 2. As we already discussed, webgrid suffers from the Connector Envy problem (Section 2) and contains an intra-boundary agglomeration (Section 3.1).
Two recent anecdotes illustrate this problem.
What examples are provided in the article that illustrate this problem?
More suggestions(15)
to articulate this problem
to highlight this problem
to illustrate this incident
to prove this problem
to illustrate this issue
to illustrate this aspect
to illustrate this dilemma
to illuminate this problem
to exemplify this problem
to underline this problem
to illustrate this effect
to illustrate this complexity
to illustrate this phenomenon
to resolve this problem
to illustrate this concept
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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