with the solutions of

USAGE SUMMARY

The phrase "with the solutions of" is correct and usable in written English.
It can be used when referring to the answers or resolutions related to a particular problem or issue. Example: "The report was compiled with the solutions of the various challenges faced during the project."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

41 human-written examples

His dissertation and much of his later work dealt with the solutions of ordinary differential equations and the associated expansions of arbitrary functions.

Encyclopedia Britannica

Moreover, the saturation capacity was reached with the solutions of higher metallic concentrations.

International Journal of Coal Science & Technology

X is the functional we needed since the critical points of X on Y coincide with the solutions of (4).

Boundary Value Problems

It is obvious that the fixed points of operator T λ coincide with the solutions of problem (16 - 17 16 - 17

Boundary Value Problems

A non-linear oscillatory problem is also solved numerically and compared with the solutions of Runge Kutta method.

Journal of Sound and Vibration

Further treatment with the solutions of H2PtCl6 and NaBH4 affords the resulting catalysts with codeposited Pt and MnO2 nanoparticles.

Electrochimica Acta

Human-verified similar examples from authoritative sources

Similar Expressions

18 human-written examples

The artist is more concerned with emotive or expressive ideas and with the solution of problems he himself poses.

Encyclopedia Britannica

The major parties came to recognize that the school struggle interfered with the solution of other problems.

Encyclopedia Britannica

These will take a back seat to the good feelings associated with the solution of a very important but secondary problem.

The New York Times

Chalmers was more concerned with the solution of human problems than with theological doctrines, and he sought to apply Christian ethics to economic issues.

Encyclopedia Britannica

A designer is basically concerned with the solution of problems (be they functional, aesthetic, or psychological) that are presented to him.

Encyclopedia Britannica

Expert writing Tips

Best practice

When using "with the solutions of", ensure the context clearly indicates what problem is being solved. Specify the problem or equation to avoid ambiguity.

Common error

Avoid using "with the solutions of" in overly general statements. Instead, focus on specific equations, systems, or problems to provide context and meaning. For example, avoid stating "the experiment was conducted with the solutions of problems" and specify which problems were solved: "the experiment was conducted with the solutions of the Navier-Stokes equations".

Linguistic Context

The phrase "with the solutions of" acts as a prepositional phrase, modifying a verb or noun by specifying how something is done or influenced by particular resolutions. Ludwig provides numerous examples across various domains where this phrase is used to connect actions or results to specific answers or resolutions.

Expression frequency: Very common

Frequent in

Science

78%

Encyclopedias

11%

Formal & Business

3%

Less common in

News & Media

2%

Reference

1%

Unknown

5%

Ludwig's WRAP-UP

In summary, the phrase "with the solutions of" is a grammatically sound prepositional phrase, commonly used in formal and scientific writing to connect actions, results, or analyses to specific answers or resolutions. Ludwig AI confirms its validity and provides ample examples. It's important to use this phrase with clear context, specifying the problem being addressed to avoid vagueness. While alternatives exist, such as "alongside the answers to" or "based on the solutions to", the choice depends on the specific nuance intended. Its prevalence in academic and scientific domains underscores its technical and precise nature.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

alongside the answers to

Focuses on the 'answers' aspect rather than the broader concept of 'solutions'.

in conjunction with the resolutions of

More formal and emphasizes the 'resolution' aspect of a problem.

based on the solutions to

Indicates that something is founded on the solutions.

using the answers from

Emphasizes the act of using the solutions to achieve something.

incorporating the answers to

Highlights the inclusion of answers in a process or outcome.

applying the resolutions from

Focuses on the application of resolutions.

through the use of the solutions for

Highlights the means by which a problem is addressed.

by means of the solutions for

Indicates a method or tool used to solve something.

utilizing the resolutions from

Emphasizes the active use of resolutions.

leveraging the answers from

Highlights using answers for strategic advantage.

FAQs

How can I use "with the solutions of" in a sentence?

Use "with the solutions of" to describe how something is achieved or influenced by the resolutions to a specific problem or equation. For instance, "The model was validated with the solutions of benchmark problems."

What are some alternatives to "with the solutions of"?

Alternatives include "alongside the answers to", "in conjunction with the resolutions of", or "based on the solutions to", depending on the specific nuance you want to convey.

Is it better to say "with the solutions of" or "using the solutions of"?

Both are correct, but "with the solutions of" often implies a more integrated or inherent relationship, while "using the solutions of" suggests a more direct application. Choose the phrasing that best reflects the nature of the connection.

What does "with the solutions of" emphasize in a sentence?

It emphasizes the role and impact of the specific solutions in the context being described. It often implies that the solutions are critical to the outcome or the process being discussed.