# Proving -|x|<x<|x|: A Homework Statement

• chocolatelover
In summary, the statement "Proving -|x|<x<|x|" means that the absolute value of x is less than x but greater than its negative. It is important to prove this statement because it helps us understand the properties of absolute value and inequalities, and allows us to solve various mathematical problems and equations. To prove this statement, one can use the definition of absolute value, properties of inequalities, and algebraic manipulation and graphing. The implications of this statement include the fact that the absolute value of any non-zero number is always positive, and that the inequality holds true for all real numbers except for x=0. An example of a problem involving this statement is solving the equation |x-5|<x-
chocolatelover

## Homework Statement

Prove that -|x|< or equal to x< or equal to|x|

## The Attempt at a Solution

I know that it is true by this example:

x=5

-5<or equal to |5|<or equal to |5|

it also hold true for x=-5

Could someone please show me or give me a hint on how to prove this?

Thank you very much

Divide and conquer: Analyze what happens when x > 0, x < 0 and x = 0.

Thank you very much

Regards