which one (s) of the following inequalities are then known to be x^2-77> 0
a) x>-5
b)x>5
c)lxl>5
this is an old exam i train and the answer shall be c) but idk how they do it.. My progress is that i solve x>sqrt(77)
I don't understand the question (probably a language issue). If X is known to be Y, then X is Y and this fact is known. None of the inequalities from the answers literally are x^2 - 77 > 0. Try rephrasing your question using the word "implies."
If $\displaystyle x^2- 77> 0$ then $\displaystyle x^2> 77$ so, taking the square root of both sides, either $\displaystyle x> \sqrt{77}$ or $\displaystyle x< -\sqrt{77}$ which is the same as $\displaystyle |x|> \sqrt{77}$. Now, $\displaystyle \sqrt{77}= 8.77$ so that $\displaystyle |x|> 8.77$. Of course, if $\displaystyle |x|> 8.77$ then it is certainly true that |x|> 5. Although that is not the "best" inequality, it is the only one of the given answers that is true.