How do you solve #(2- 3x ) ( x^{3} + 4x ) \leq 0#?

1 Answer
Gazza
Oct 24, 2017

#x<-1.587401 or x>=2/3#

Explanation:

#(2-3x)(x^3+4)<=0#
Use the distributive property.
#(2)(x^3)+(2)(4)+(-3x)(x^3)+(-3x)(4) <=0#
#2x^3 + 8 - 3x^4 - 12x <=0#
#-3x^4 +2x^3 - 12x + 8 <=0#
Let's find the critical points of the inequality.
#-3x^4 +2x^3 -12x+8 =0#
Factorize the left side
#(-3x+2)(x^3+4)=0#
Set factors equal to 0
#-3x + 2=0 or x^3 +4=0#
#x=2/3 or x=-1.587401#

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