An Absolute-Value Inequality

★ 7/10Absolute Value algebra inequality Casework

Problem

Prove that for all reals $a, b, c$ ,

|a| + |b| + |c| + |a+b+c| \ge |a+b| + |b+c| + |c+a|,

and determine exactly when equality holds.

Answer

Solution

Difficulty	7/10
Topics	Absolute Value, algebra, inequality, Casework

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