Modulus Inequalities (Absolute Value Inequalities): Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
$|x^2+2x-4|>4$
Problem 2
$x^2+|6x-24| \le 16$
Problem 3
$|x+3|+|x-4| \ge 11$
Problem 4
$|x^2-1| < x^2-|x|+1$
Problem 5
$|x^2-2x-3|+2|x-2|<5$
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