Algebra · Absolute value · Inequalities · Relations · Equality case
Problem 1, 2020
A relation \(\diamond\) is defined on the set \(\mathbb{R}\) of real numbers by
\[ a \diamond b \quad \text{if and only if} \quad |a - 1| + |b - 2| \leqslant 1 . \]
Suppose the real numbers \(x\) and \(y\) satisfy both \(x \diamond (y - x)\) and \(x \diamond (y + x)\). Determine \(y\).
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Serbian Regional Competition (Okruzno takmicenje) 2020, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source