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Prove that $||a|-|b||\leq|a-b|$ .

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Lesson Parent:

Problem:

Prove that
$\begin{equation} \left| |a|-|b| \right|\leq\left| a-b\right|. \end{equation}$

Answer:

It is true that $\begin{equation} \left| |a|-|b| \right|\leq\left| a-b\right|. \end{equation}$

Solution:

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

and therefore