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.
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?
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.