1. Prove ||a|-|b||≤ |a-b|

Can someone solve this problem?

PROVE: For any real numbers a and b ||a|-|b||≤ |a-b|

2. You need to know the triangular inequality.

$|a| = |a - b + b|$

$= |(a - b) + b|$

$\leq |a - b| + |b|$.

Since $|a| \leq |a - b| + |b|$

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

If we take the modulus of both sides, we have

$\left||a| - |b|\right| \leq \left||a - b|\right|$

$\left||a| - |b|\right| \leq |a - b|$.