Question

how to solve this inequalities x2-7x-8>0

Answer 1

First, you should try to factorize the second grade polinomy,
\[x^2-7x-8=(x+1)(x-8)\]
Then you can solve this,
\[(x+1)(x-8)>0\]
looking for the sign of this equation in this way,
\[\text{if}\ \ x<-1\Rightarrow -\cdot - =+\]
\[\text{if}\ \ 8>x>-1\Rightarrow +\cdot - =-\]
\[\text{if}\ \ x>8\Rightarrow +\cdot + =+\]
So the only region where the equation is <0 is the interval (-1,8).