Why is $5x+10=2$ not a proposition? Why is $5x+10=2$ not a proposition?
My textbook says, "a proposition is any statement that is true or false and its truth value can be known, unknown, true, false, or a matter of opinion".
By that definition, $5x+10=2$ should be a proposition because the truth value is "unknown".
I'm trying to submit some answers into my online homework software and it's telling me that $5x+10=2$ is not a proposition.
Thanks in advance.
 A: I see where you're coming from, but that is not what the definition means by "unknown".  They are thinking of a statement like "Every even integer greater than 4 can be expressed as the sum of two primes".  That is definitely either true or false, but we don't know which one.
$5x+2=10$ is a statement whose truth or falsity depends on the value of the variable $x$, so this is a very different situation.  I would use the word "predicate" to describe this situation, but your textbook or teacher may have a different idea of how the vocabulary shakes out.
A: To be proposition it must be either true or false , not both of them or neither.
When we place some number in $x$ it is true such as $-8/5$ ,but it is false for $R- \{-8/5 
 \}$
When we comes to main question , i.e unknown part. When we talk about unknown , it is wanted to mean that proposition it either true or false but we do not know which one such that $5589746$ bird is given birth last year is a proposition , because it is either true or false but we actually do not know which.
The other example is that "there are aliens in milkyway", it is either true or false but its truth value is unknown
A: It's not a proposition but a statement form instead.  Simply read it out loud: "Five times as much as a number, increased by two, gives ten."  This sentence isn't a statement as it can't be neither true or false at all as long as you don't replace the placeholder "a number" by a certain number.
Replace it with 8, e.g., and then a statement is produced, namely: "Five times as much as $8$, increased by two, gives $10$."  That's a statement, a false on, of course.  Now the set of all replacements which will produce a true statement is called the solution set of the statement form.
See also Question about an equatuon with 2 unknowns?
