Answer to Question #236782 in Calculus for CCW

Question

Polynomial Inequalities:

7) 12 - x - x^2 < 0

show number line and answer in interval notation

Answer 1

12-x-x²<0

12-4x+3x-x²<0

4(3-x)+x(3-x)<0

(4+x)(3-x)<0

4+x<0

x<-4

3-x<0

-(x-3)<0

(x-3)>0

x>3

answer in interval notation;

$x=(-\infty,-4) U (\infty,3)$