Prove that -|x| ≤ x ≤ |x| for any real number

[mindauggas]

Homework Statement

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

Homework Equations

Only the definition of absolute value is allowed.

The Attempt at a Solution

Don't even know where to start

 

[mtayab1994]

First prove -lxl≤x then prove x≤lxl

 

[LCKurtz]

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

 

[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