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a)
[tex]\boxed{|3x-1|<2}\ \therefore\[/tex]
[tex]i)\ 3x-1<2\ \therefore\ 3x<3\ \therefore\ x<1[/tex]
[tex]ii)\ 3x-1>-2\ \therefore\ 3x>-1\ \therefore\ x>-\dfrac{1}{3}[/tex]
[tex]\boxed{\mathbb{S}=\left\{x\in\mathbb{R}\ |\ -\dfrac{1}{3}<x<1\right\}}[/tex]
b)
O mesmo que a resolução anterior.
c)
[tex]\boxed{|x+3|>1}\ \therefore[/tex]
[tex]i)\ x+3>1\ \therefore\ x>-2[/tex]
[tex]ii)\ x+3<-1\ \therefore\ x<-4[/tex]
[tex]\boxed{\mathbb{S}=\left\{x\in\mathbb{R}\ |\ x\in(-\infty,-4[\cup]-2,\infty)\right\}}[/tex]
d)
[tex]\boxed{|x+1|<|2x-1|}\ \therefore[/tex]
[tex]i)\ x+1=2x-1\ \therefore\ x=2[/tex]
[tex]ii)\ x+1=-(2x-1)\ \therefore\ x+1=-2x+1\ \therefore\ x=0[/tex]
[tex]x<0\ \to\ \text{p. ex.}\ x=-1\ \to\ 0<3\ \to\ \text{Ok.}\\\\ 0<x<2\ \to\ \text{p. ex.}\ x=1\ \to\ 2\nless1\\\\ x>2\ \to\ \text{p. ex.}\ x=3\ \to\ 4<5\ \to\ \text{Ok.}[/tex]
[tex]\boxed{\mathbb{S}=\left\{x\in\mathbb{R}\ |\ x\in(-\infty,0[\cup]2,\infty)\right\}}[/tex]
e)
[tex]\boxed{|x-3|<x+1}\ \therefore[/tex]
[tex]i)\ x-3=-(x+1)\ \therefore x-3=-x-1\ \therefore\ x=1[/tex]
[tex]x<1\ \to\ \text{p. ex.}\ x=0\ \to\ 3\nless1\\\\ x=1\ \to\ 2\nless2\\\\ x>1\ \to\ \text{p. ex.}\ x=2\ \to\ 1<3\ \to\ \text{Ok.}[/tex]
[tex]\boxed{\mathbb{S}=\left\{x\in\mathbb{R}\ |\ x\in]1,\infty)\right\}}[/tex]
f)
Incompleto. Não é possível resolver.