Mod inequality

[SuperTramp]

help please

How do you solve
|x+2|<|3x+1|

Thanx

[KatieB]

help please

How do you solve
|x+2|<|3x+1|

Thanx
square both sides
(x+2)<(3x+1)
x+4x+4<9x+6x+1
0<8x+2x-3
8x+2x-3>0
(4x+3)(2x-1)>0
critical values x=-3/4 or x=1/2
draw the quad graph of y=8x+2x-3 and see where it is above the x axis
ie. x<-3/4 or x>1/2

[talkingturtles]

There is actually an easier way! All you have to do is solve the 2 equations below:

x+2<3x+1

x+2<-(3x+1)

To get:

x>½
x<-¾

Its easier cuz u dnt av 2 mess about with quadratics!

[samee380]

both ways are good. go for the talkingturtles method as then you can solve any equation with mod signs i.e. |2x + 3| = 3

squaring both sides wont be very effecient with the above equation. sometimes it works but not always