Final answer:
A proposition must be a statement with a truth value, meaning it can be true or false. 'Let's watch a movie' is not a proposition, while 'x-7>0' can be a proposition under specific conditions such as a known value for x. In algebra, propositions are often found in equations where relationships between variables are asserted.
Step-by-step explanation:
To determine whether each statement is a proposition, we need to identify if the statement has a truth value, meaning it can either be true or false. The statement 'Let's watch a movie' is not a proposition because it is an imperative sentence expressing a suggestion or command rather than stating a fact that can be true or false. On the other hand, the inequality 'x-7>0' can be considered a proposition if the variable x represents a specific number because then the inequality can be tested for truthfulness. If, however, x is just a placeholder without a specific value, it does not qualify as a proposition.
Predicates play a role in determining propositions. A predicate clarifies the conditions under which a sentence can be true. For example, in the inequality 'x-7>0', if x is known to be greater than 7, then the inequality can be seen as true, making it a proposition.
There are several steps one might take in simplifying algebra and ensuring reasonable answers, such as eliminating terms wherever possible to simplify the algebra and always checking the answer to see if it is reasonable. In the context of algebraic equations like '7y = 6x + 8', we are typically dealing with propositions as they make declarative statements about the relationships between variables that can be deemed true or false.