ccooley
I'm glad you raised this question. It turns out that there are two different scenarios:
\(\sqrt{9}=x\)
\(9 = x^2\)
Those are two different things on the GMAT.
Those are two different things everywhere, not just on the GMAT. I bring this up because there seems to be a persistent misconception in GMAT prep circles that there is such a thing as "GMAT math" -- a set of math rules or conventions you need to learn specifically for this test. That's not true; GMAT math is exactly the same as the math you'd learn in any other math course (within the bounds the GMAT specifies, e.g. that all numbers are real numbers), so everything test takers learn about math during GMAT prep will potentially also be useful when they're doing math in their MBA or elsewhere.
dave13
i wonder why arent you considering two cases for this inequality \(\sqrt{(x+1)^2} <= \sqrt{36}\)
|x+1| <= 6
i thought there should be TWO cases to consider - positive and negative x+1<= 6 and x+1 >= -6
because \(\sqrt{x^2} =|x|\) which means x can be negative or positive
Just like with this equation (x-1)^2=400
Another question what if we had such inequity (10-x)^2 <= 9 would there be two cases ? i lay stress in this inequality on X being negative, very doubt if inequality is correct

It looks like Karishma didn't finish solving the problem in that post. If you do see the inequality:
|x + 1|
< 6
then x+1 must be somewhere between -6 and 6 (inclusive), so x itself is somewhere between -7 and 5 inclusive. It's certainly possible that x is negative, and you must consider that possibility to get the right solution set.
Similarly if you know (10 - x)^2
< 9, then 10 - x must be somewhere between -3 and 3 inclusive. If you then simplify the two inequalities 10 - x
> -3 and 10 - x
< 3, you find 7
< x
< 13.