Prove that ||a|−|b||≤|a−b|.

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Lesson Parent: 
Rules of Absolute Values
Problem: 

Prove that
||a|−|b||≤|a−b|.

Answer: 

It is true that ||a|−|b||≤|a−b|.

SAMPLE SOLUTION

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Solution: 

We know that <Sign in to see all the formulas>. Let's do some algebra:

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We used the fact that <Sign in to see all the formulas> to get the last equation. Using this fact again we see that

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and therefore

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