Question

a solução da equação |3x+1| = |x-3| é?
a) {-2, -1/3}
b) {-2, 1/2}
c) {1/3}
d) {-1/3}
e) nda​

Answer 1

Propriedade do módulo

$\mathsf{|a|=|b|\Leftrightarrow\,a=b\:ou\,a=-b}$

$\mathsf{3x+1=x-3}\\\mathsf{3x-x=-3-1}\\\mathsf{2x=-4\rightarrow\,x=-\dfrac{4}{2}=-2}$

$\mathsf{3x+2=3-x}\\\mathsf{3x+x=3-2}\\\mathsf{4x=1\rightarrow\,x=\dfrac{1}{4}}$

$s=\{(-2,\dfrac{1}{4})\}$