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x in (-oo:+oo)
abs((3*x-2)/2) < 5 // - 5
abs((3*x-2)/2)-5 < 0
abs((3*x-2)/2)-5 < 0
x in (-oo:+oo)
abs((3*x-2)/2)
(3*x-2)/2 >= 0
( 2 )
2 >= 0
x należy do R
( 3*x-2 )
3*x-2 >= 0 // + 2
3*x >= 2 // : 3
x >= 2/3
(-oo:2/3) (2/3:+oo) 2 + + 3*x-2 - +
x in <2/3:+oo)
(3*x-2)/2-5 < 0
x in (-oo:2/3)
-((3*x-2)/2)-5 < 0
abs((3*x-2)/2)-5 < 0
/ | -((3*x-2)/2)-5 < 0 i x in (-oo:2/3) | (3*x-2)/2-5 < 0 i x in <2/3:+oo)
x in (-oo:2/3)
-((3*x-2)/2)-5 < 0
(-1*(3*x-2))/2-5 < 0
(-1*(3*x-2))/2+(-5*2)/2 < 0
-1*(3*x-2)-5*2 < 0
-3*x-8 < 0
(-3*x-8)/2 < 0
(-3*x-8)/2 < 0 // * 2^2
2*(-3*x-8) < 0
( -3*x-8 )
-3*x-8 < 0 // + 8
-3*x < 8 // : -3
x > 8/(-3)
x > -8/3
( 2 )
2 < 0
x belongs to the empty set
(-oo:-8/3) (-8/3:+oo) -3*x-8 + - 2 + +
x in <2/3:+oo)
(3*x-2)/2-5 < 0
(3*x-2)/2+(-5*2)/2 < 0
3*x-5*2-2 < 0
3*x-12 < 0
(3*x-12)/2 < 0
(3*x-12)/2 < 0 // * 2^2
2*(3*x-12) < 0
( 2 )
2 < 0
x belongs to the empty set
( 3*x-12 )
3*x-12 < 0 // + 12
3*x < 12 // : 3
x < 12/3
x < 4
(-oo:4) (4:+oo) 2 + + 3*x-12 - +
x in (-8/3:4)
(-8/3:4)
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