EIV, Chapter6, Q#1 (p121) - please help!

[hs-hop]

Hi, I'm a little confused about inequalities.

Here is the Q#1 of inequalities problem set (EIV, Chapter6, p121)

Q:If 4x-12=>x+9, which of the following must be true?
(A) x>6 (B) x<7 (C) x>7 (D)x>8 (E) x<8

OA: 4x-12=>x+9
3x=>21
x=>7 If x=>7, then x>6
I understand the above statement if x was an integer (which is not stated in the question), but if that is not the case, wouldn't (C) be the correct answer?
Or is it possible that I'm misunderstanding the question?
My logic was that, for a choice to be "must be true", its condition needs to be included in the premise (x=>7), but I realize that this will include both (C) and (D).

Someone please help me! Thanks,

[esledge]

My logic was that, for a choice to be "must be true", its condition needs to be included in the premise (x=>7), but I realize that this will include both (C) and (D).

You were close: For a choice to be "must be true," the premise (x>=7) must be included in the choice (the reverse of what you said).

Look at it this way: The premise allows x = 7 as a possible answer. Only choices (A) and (E) allow x = 7 as well, and we can eliminate (E) for including non-valid x values. Choices (C) and (D) might be true, but are not "must be true" choices because we can find some valid x solutions that are not included in those ranges.