write a quadratic inequality whose solution is x<3 or x>7?

Question

steps please...

Answer 1

Quadratics are easier to deal with when they're factored. And everything's easier when one side of the inequality is 0.

Well, maybe we can find f and g such that f*g>0 satsifies the inequality by having it be the case that:

f >0 if and only if x >3 and
g>0 if and only if x >7.

The idea is that first (i.e., when -infinity
Well, let f = x-3 and g = x-7.

I.e., (x-3)(x-7)>0 does the job.