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The phrase "achieves this purpose" is correct and usable in written English.
You can use it when discussing how something successfully fulfills a specific goal or intention.
Example: "The new marketing strategy achieves this purpose by targeting a younger demographic."
Alternatives: "fulfills this objective" or "meets this aim."
Exact(4)
It achieves this purpose by using a series of matrices.
For extremely fine coal, a process called flotation achieves this purpose.
However, this new distribution with one parameter and simple form of cdf achieves this purpose.
Every soul mate we meet achieves this purpose.
Similar(56)
He asked President Clinton to help achieve this purpose.
In other instances the entire chain must be intact to achieve this purpose.
To achieve this purpose two learning techniques are used.
Roosevelt assented, and a bill to achieve this purpose was passed by the Congress in early 1941.
The ability to forge connections and relationships through small talk is a critical tool for achieving this purpose.
To achieve this purpose, local information in a form of optical strain measurement is employed.
To achieve this purpose, 19 mortar mixtures with different heterogeneity and strength characteristics were tested.
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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