Question 1 in chapter 6 of the VIC strategy guide asks:

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

the answer provided is A.

why is that the answer? when solved for x, x>=7, so x must be at least 7. shouldn't the answer be D? if you try 6.1, then the inequality doesn't hold true. what am i missing here?

You did the math right - but you fell down on the logic of the question itself. This test is tricky!

Yes, x >=7. The questions asks what MUST be true when x>=7. If I choose D, as you suggest, then I'm saying x MUST BE greater than 8. Is that true? No, it could be 7 or between 7 and 8. Likewise, if I choose C, then I'm saying x MUST BE greater than 7, but that's not true either - x could be 7.

If I choose A, I'm saying x MUST BE greater than 6. I'm not actually saying that x IS or even could be 6.1 (or anyting between 6 and 7). I'm saying that whatever x is, that number MUST BE greater than 6. And that's true - 7, between 7 and 8, 8, larger than 8 - those are all greater than 6.

Be careful with the wording of the question! They do not ask things in the straightforward way that we're used to being asked on typical school math tests. If they had asked "what is the range of possible values for x?" then the right answer would've been x>=7 (though that's not in the choices here - which can be a clue that we need to think about this logically and not just mathematically!).