sanatakesGMAT
Hi experts, I had a doubt here.
we get the final equation as 9>x>-3
however the answer here is C. x>-4
which doesn???t make sense to me since if x>-4, then -3 could also be a possible solution for x, which according to our solution is wrong (x must be greater then -3)
Please let me know if im missing some logic here.
Tricky question and I can see how this is confusing. First, note that the question says
must be true which to me a huge signal for
Testing Cases. I'm going to reorganize the solution so that we're going small -> large left to right (like a number line).
KNOWN: -3 < x < 9
So this means that all real values of x must fit in that range. Let's test some cases in that range and see which answer choices we can eliminate! Start with some extremes in the range:
Test: x = -2.9999 (smallest end)
This is a legal value of x, which means that x doesn't have to be greater than 0.
Eliminate A and D. Test: x = 8.9999 (largest end)
This is a legal value of x, which means that x doesn't have to be less than 8.
Eliminate B.What is left? C and E
We could test something in the middle, but notice that from the smallest to the highest number in this list, everything is greater than -4. So it is true that x > -4. Note that it would also be true that everything in the list is greater than -5 or -6 or -1000 or -1 million and so on. The reason that C works is because the entire range of x is definitely greater than -4!
Choose C!Hope this helps!

Whit