Question

Rezolvati in multimea numerelor intregi nenule inecuatia |x-2|(7-|2x-1|)>0

Answer 1

!x-2!(7-!2x-1!)>0 / : !x-2! (modulul este nr. pozitiv)
7-!2x-1!>0 / -7
-!2x-1! > -7
!2x-1!<7
-7<2x-1<7 /+1
-6<2x<8 /:2
-3<x<4
x=(-3,4)
APP...am folosit semnul exclamarii in loc de modul pt c mie nu-mi merge tasta :)))

Answer 2

|x-2|(7-|2x-1|)>0
|-2|<0
7-|2x-1|<0
|x-2|>0
7-|2x-1|>0
7-|2x-1|<0
|x-2|>0
7-|2x-1|>0
x-2=≠0
7-|2x-1|>0
x≠2
7-|2x-1|>7
x≠2 -|2x-1|>-7
x≠2
2x-1<7
2x-1>-7
x≠2
2x<7+1
2x-1>-7 
x≠2 
2x<8
2x-1>7
x≠2
x<8:2
2x-1>-7
x≠2
x<4
2x>-7+1
X≠2
x<4
x>-6:2
x≠2
x∉{-3,4}
x∉{-3,2}U{2,4}