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x in (-oo:+oo)
(1/6)*x-8 < (1/2)*x-(3/2) // - (1/2)*x-(3/2)
(1/6)*x-((1/2)*x)+3/2-8 < 0
(1/6)*x+(-1/2)*x+3/2-8 < 0
-1/3*x-13/2 < 0 // + 13/2
-1/3*x < 13/2 // : -1/3
x > 13/2/(-1/3)
x > -39/2
x in (-39/2:+oo)
(-39/2:+oo)
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