Modulus equations (Absolute Value Equalities): Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
$|x^2-5x|=6$
Problem 2
$|x|=x+2$
Problem 3
$2|x+1|+1=3$
Problem 4
$|4-|x||=2$
Problem 5
$|x-1|+|x-2|=1$
Problem 6
$|2x-1|+|3x+2|=3-|x|$
Problem 7
$|2x+3|=|2x^2-x-1|+1$
Problem 8
$|2-x|+|3x-1|=5x-2|x-4|$
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