Say for example we considered something like \(\displaystyle \frac{1}{(x+3)^3} > 1000\). It's possible for \(\displaystyle (x+3)^3\) to be a negative number, but if it was negative, the value on the left-hand side would have been negative, and a negative number can't be greater than 1000. So we just need to make a side note that we are only considering values of \(\displaystyle x\) such that \(\displaystyle x>-3\). From then we can continue the problem.

As for your second question: Any time you take an even-powered root of a value, you must take its absolute value. In other words: