Question

Determine as raízes da equação modular |5x- 11|=|x+7|

Answer 1

$|5x-11|=|x+7|$

$\text{Caso 1:}$

$5x-11=x+7\ \therefore\ 4x=18\ \therefore\ \boxed{x=\dfrac{9}{2}}$

$\text{Caso 2:}$

$5x-11=-(x+7)\ \therefore\ 6x=4\ \therefore\ \boxed{x=\dfrac{2}{3}}$

$\mathrm{Solu\c{c}\tilde{a}}\text{o:}$

$x=\left\{\dfrac{2}{3},\dfrac{9}{2}\right\}$