Question

(x+4)(x^2+8x+16)(4x^2-9)≥0

Answer 1

x=-4 three repeats, and x=-3/2 and x=3/2

Answer 2

this is an inequality

Answer 3

so x>=-4 three repeats, and x<=-3/2 and x>=3/2

Answer 4

(x+4)^3(2x+3)(2x-3)>=0 implies (x+4)(2x+3)(2x-3)>=0 so
x in {-4, -3/2, 3/2} for boundary
(x+4)(2x+3)(2x-3) well ++>0 +-<0 -->0 therefore +++>0 and +-->0 so either they're all positive or two are negative
x+4>0 and 2x+3>0 and 2x-3>0 -> x>-4 and x>-3/2 and x>3/2 -> x>3/2
x+4>0 and 2x+3<0 and 2x-3<0 -> x>-4 and x<-3/2 and x<3/2 -> -4<x<-3/2
x+4<0 and 2x+3<0 and 2x-3>0 -> x<-4 and x<-3/2 and x>3/2 -> {}
x+4<0 and 2x+3>0 and 2x-3<0 -> x<-4 and x>-3/2 and x<3/2 -> {}
therefore the solution is in {-4,-3/2,3/2} or x>3/2 or -4<x<-3/2 i.e. x>=3/2 or -4<=x<=-3/2

Answer 5

it should be in interval :