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

  • Thread starter chocolatelover
  • Start date
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-
  • #1
chocolatelover
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Homework Statement


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


Homework Equations





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
 
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  • #2
Divide and conquer: Analyze what happens when x > 0, x < 0 and x = 0.
 
  • #3
Thank you very much

Regards
 

1. What does the statement "Proving -|x|

The statement means that the absolute value of x is less than x but greater than its negative. In other words, x is a non-zero number that is greater than its negative value.

2. Why is it important to prove this statement?

Proving this statement is important because it helps us understand the properties of absolute value and inequalities. It also allows us to solve various mathematical problems and equations.

3. How can I prove this statement?

To prove -|x|

4. What are the implications of this statement?

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. It also helps to understand the concept of symmetry in equations involving absolute value.

5. Can you provide an example of a problem involving this statement?

One example of a problem involving this statement is solving the equation |x-5|

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