Is "Inequality (1) infers" correct? (as in "Inequality (1) holds/follows")

Solution 1:

"Inequality (1) infers..." would be considered an error in academic publishing (e.g., the Springer–Nature and Elsevier families of journals), including mathematics articles.

(I'll leave aside the question of whether "infer" can ever legitimately, in other contexts, be used to mean "imply" based on historical usage.)

Modern dictionaries distinguish that only a person can infer a result (e.g., through derivation from reason). In a conventional journal article, inequality (1) may hold, it may follow, it may imply, or it may be inferred, but it can't infer.

If you find multiple such errors, it's reasonable to ask the authors to have their manuscript professionally edited before resubmission.

Solution 2:

• Inequality (1) infers.
• Inequality (2) infers from the fact that...

It is not correct to say that an inequality or any sort of mathematical concept "infers" something. the usual term is "implies".

• Inequality (1) can be inferred.
• Inequality (2) can be inferred from the facts that...

The type of the second sentence seems much more common.