Signs from an Absolute Inequality

Problem

Real numbers $a,b$ satisfy

\bigl||a|-(a+b)\bigr|<\bigl|a-|a+b|\bigr|.

Determine the sign of $a$ and the sign of $b$ (each $>0$ or $<0$ ).

Answer

Solution

Difficulty	7/10
Topics	Absolute Value, algebra, inequality

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