# Absolute Values

1. Feb 20, 2014

### TheRedDevil18

1. The problem statement, all variables and given/known data

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

|x-3| < 2|x|

2. Relevant equations

3. 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

2. Feb 20, 2014

### 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)?

3. Feb 20, 2014

### LCKurtz

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