The reason the sentence “\(3 + x = 12\)” is not a statement is that it contains a variable. Depending on what \(x\) is, the sentence is either true or false, but right now it is neither. One way to make the sentence into a statement is to specify the value of the variable in some way. This could be done by specifying a specific substitution, for example, “\(3+x = 12\) where \(x = 9\text{,}\)” which is a true statement. Or you could capture the free variable by quantifying over it, as in, “for all values of \(x\text{,}\) \(3+x = 12\text{,}\)” which is false. We will discuss quantifiers in more detail at the end of this section.
in-context