Algebra · Absolute value · Rational inequalities · Case analysis · Sign of a quotient · Intervals
Find all real numbers \(x\) that satisfy the inequality
\[ \frac{|x-3| + x}{x+1} < 1 . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2018, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source