There exists a real number x such that 2x+5 = 10.
This is a statement because either such a real number exists or such a real number does not exist. In this case, this is a true statement since such a real number does exist, namely x = 2.5.
For each real number x, 2x +5 = 2 x + 5/2
This is a statement since either the sentence 2x +5 = 2 x +
5/2 is true when any real number is substituted for x (in which case, the statement is true) or there is at least one real number that can be substituted for x and produce a false statement (in which case, the statement is false). In this case, the given statement is true.
