How do you solve #x^3<x^2# using a sign chart?

1 Answer
Oct 22, 2016

Answer:

#x ∈)-oo,0(∪)0,1 (#

Explanation:

Rewrite the equation as #x^3-x^2<0#

on factorization, #x^2(x-1)<0#

the points we have to look at are #x=0# and #x=1#

here is the sign chart

#x# #color(white(aaaaaa))# #-oo# #color(white)(aaaa)# #0# #color(white)(aaaaaaaaa)# #1# #color(white)(aaaaaa)# #+oo#
#x##color(white)(aaaaa)##-##color(white)(aa)# #0##color(white)(aaaa)##+##color(white)(aaaaaaa)##+#
#x^2##color(white)(aaaa)##+##color(white)(aa)# #0##color(white)(aaaa)##+##color(white)(aaaaaaa)##+#
#x-1##color(white)(aa)##-##color(white)(aa)# #color(white)(aaaaa)##-##color(white)(aaa)##0##color(white)(aa)# #color(white)(aa)##+##color(white)(aaa)#
#x^2(x-1)##-##color(white)(aaaaa)# #-##color(white)(aaaaaaaaa)##+#

So the answer is #x ∈)-oo,0(∪)0,1 (# for #x<0#