How do you solve #| 3 + 2x | >| 4 - x |#?

1 Answer
Jul 22, 2017

Answer:

# x<-7 or x>1/3#

Explanation:

#abs(3+2x)>abs(4-x)#
Since both sides are positive
You can do the square at both sides to get rid of the abs sign
#because (abs(x))^2=(x)^2#

#(abs(3+2x))^2>(abs(4-x))^2#
#(3+2x)^2>(4-x)^2#
#9+12x+4x^2>16-8x+x^2#
#3x^2+20x-7>0#
#(3x-1)(x+7)>0#

#color(white)(....)#+#color(white)(..............)##-##color(white)(..................)##+#
<--------#@##color(white)(......................)##@#-------------->
----------/--------------------------/-----------------
#color(white)(.....)##-7##color(white)(.......................)##1/3#

#therefore x<-7 or x>1/3#