Question

O número de solução inteiras da inequação |3x-5| <4 é:
A) 2
B) 3
C) 4
D) 5
E) 6

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Desigualdades\,envolvendo\,m\acute odulos.}\\\sf\bullet \!~|x|>a\longrightarrow x<-a~ou~x>a\\\sf\,\bullet\,\,|x|<a\longrightarrow -a<x<a\\\sf\,\bullet~|x|\geqslant a\longrightarrow x\leqslant -a~ou~x\geqslant a\\\sf\,\bullet\,\,|x|\leqslant a\longrightarrow -a\leqslant x\leqslant a\end{array}}$

$\large\boxed{\begin{array}{l}\sf |3x-5|<4\\\sf usando\,a\,2^a\,desigualdade\,temos:\\\sf -4<3x-5<4\\\sf -4+5<3x<4+5\\\sf 1<3x<9\\\sf\dfrac{1}{3}<x<3\\\\\sf (1,2)\\\huge\boxed{\boxed{\boxed{\boxed{\sf\dagger\red{\maltese}~\blue{alternativa~B}}}}} \end{array}}$