Are there real numbers $a, b$ and $c$ such that for all real $x$ and $y$ the following inequality holds: $$|x + a| + |x + y + b| + |y + c| > |x| + |x + y| + |y|?$$
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Tags: algebra, inequalities
Are there real numbers $a, b$ and $c$ such that for all real $x$ and $y$ the following inequality holds: $$|x + a| + |x + y + b| + |y + c| > |x| + |x + y| + |y|?$$