How do you solve #x^3<9x#?

1 Answer
Jul 24, 2016

Answer:

#color(green)(x in (0,3))# or #color(green)(x in (-oo,-3))#

Explanation:

Given
#color(white)("XXX")x^3 < 9x#

Note that the equation can not be true if #x=0#

Case 1: #color(black)(x > 0)#
#color(white)("XXX")x^2 < 9#
#color(white)("XXX")rarr x < 3#
therefore #x in (0,3)#

Case 2: #color(black)(x < 0)#
#color(white)("XXX")x^2 > 9# (remember when dividing by a negative the inequality is reversed)
#color(white)("XXX")abs(x) > 3#
and since #x < 0#
#color(white)("XXX")rarr x < -3#
therefore #x in (-oo,-3)#