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

1 Answer
Jul 22, 2017

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)(.....)-7color(white)(.......................)1/3

therefore x<-7 or x>1/3