# Help in absolute value question?!

##
Solve #|2x-1|<|x|# .

I understand that the correct answer is #1/3<=x<=1# , however I do not understand that when you apply:

#2x-1<0# and #x<0# ,

the answer comes out as #x>= 1# , which is not the answer.

Please explain?

Solve

I understand that the correct answer is

the answer comes out as

Please explain?

##### 1 Answer

Below

#### Explanation:

Draw the functions

graph{(y-abs(2x-1))(y-absx)=0 [-10, 10, -5, 5]}

Now, hopefully you can see that the two functions cross each other at 2 different points.

To find your 2 points, you have to know which lines to use. Going from the right, the equations of each lines are:

#y=x# #y=2x-1# #y=-(2x-1)# #y=-x#

Looking at the graph, you can see that the line

Finding the 2 points,

Therefore, the line

Hence, the answer is