Algebra · Absolute value · Inequalities · Case analysis · Piecewise linear functions
Find every real number \(x\) that satisfies
\[ \Bigl|\, \bigl|\, |2-x| - x \,\bigr| - 8 \,\Bigr| \le 2008 . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2008, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source