[sykh]

There is a solution. An equation is really a question.

x+3 = 1

is asking the question, “what value for x makes x+3 the number 1?”

The polynomial x+3 is defined for all values in R, the base ring you are working in. We are trying to find the elements of R for which x+3 is the element 1.

[jcranberry]

An equation is an instance of equating.

A solution necessitates a question, and questions associated with equations involving variables aren't restricted to: what is set of possible values which satisfy those equations?

[sykh]

You are incorrect. This is not how mathematicians view a polynomial equation like the one I used as an example. That equation does have a solution.