Solving an Inequality: |x-3| < 2|x|

[TheRedDevil18]

Homework Statement

Solve the given inequality by interpreting it as a statement about distances in the real line:

|x-3| < 2|x|

Homework Equations

The Attempt at a Solution

I have no clue what to do here and I do not understand the answer in the textbook

Goes something like this.....
x^2 - 6x + 9.....Have no idea how they got that
= (x-3)^2
...and so forth

 

[shortydeb]

There are two possibilities for x: either x is greater than or equal to 3, or x is less than 3.

If x ≥ 3, what does the inequality look like (i.e. without the absolute value)?

 

[LCKurtz]

Homework Statement

Solve the given inequality by interpreting it as a statement about distances in the real line:

|x-3| < 2|x|

Homework Equations

The Attempt at a Solution

I have no clue what to do here and I do not understand the answer in the textbook

Goes something like this.....
x^2 - 6x + 9.....Have no idea how they got that
= (x-3)^2
...and so forth

They used $|a|<|b| \leftrightarrow a^2<b^2$.