# Proof of an expression involving absolute value

1. Dec 17, 2011

### mindauggas

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

Prove: for any real number x, -|x|$\leq$x$\leq$|x|.

2. Relevant equations

Only the definition of absolute value is allowed.

3. The attempt at a solution

Don't even know where to start

2. Dec 17, 2011

### mtayab1994

First prove -lxl≤x then prove x≤lxl

3. Dec 18, 2011

### LCKurtz

Also consider breaking the problem into two cases, where x ≥ 0 and x < 0.

Last edited: Dec 18, 2011
4. Dec 18, 2011

### genericusrnme

pretty much what mtayab and LCKurtz said
first take x greater than zero, take x less than zero and take x equal to zero

this method is called a proof by exhaustion