Question

Resolva a equaçao modular em R

Answer 1

Olá,

aplique o conceito de módulo:

$\left| \dfrac{2-x}{4}\right|=x-1~~~~~~~~e~~~~~\left| \dfrac{2-x}{4}\right|=-(x-1)\\\\\\ \dfrac{2-x}{4}=x-1~~~~~~~~~e~~~~~ \dfrac{2-x}{4} =-x+1\\\\ 2-x=4\cdot(x-1)~~~~e~~~2-x=4\cdot(-x+1)\\ 2-x=4x-4~~~~~~~~~e~~~~2-x=-4x+4\\ 5x=6~~~~~~~~~~~~~~~~~~~e~~~~~~-3x=-2\\\\ x= \dfrac{6}{5} ~~~~~~~~~~~~~~~~~~~~e~~~~~~~~x= \dfrac{2}{3}~~\notin~\mathbb{R}$

Portanto,

$\text{S}=\left\{ \dfrac{6}{5}\right\}$