What is 9-|x+4|<5 in set and interval notation?

Answer 1

9-|x+4| < 5
|x+4| > 4
so x is more than 4 units away from -4:
(-∞,-8)U(0,∞)
{xεR||x+4|>4}

algebraically,
|x+4| > 4
case I (x+4)>0 ; x > -4
x+4 > 4
x > 0
case II (x+4)<0 ; x < -4
-(x+4) > 4
x+4 < -4
x < -8