ОДЗ
{3x-1>0⇒x>1/3
{3x-1≠1⇒x≠2/3
x∈(1/3;2/3) U (2/3;∞)
1)x∈(1/3;2/3)
(3x-1)²<16<br>(3x-1)²-16<0<br>(3x-1-4)(3x-1+4)<0<br>(3x-5)(3x+3)<0<br>x=5/3 x=-1
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+ _ +
-------(-1)------(1/3)---------(2/3)----(5/3)----------------
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x∈(1/3;2/3)
2)x∈(2/3;∞)
(3x-1)²>16
(3x-5)(3x+3)>0
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+ _ +
-------(-1)------(1/3)---------(2/3)----(5/3)----------------
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x∈(5/3;∞)
Ответ x∈(1/3;2/3) U (5/3;∞)