Question

Função modular

||2x-1|-5|=0

Answer 1

Olá Jackson!

$\\ \mathsf{|\underbrace{\mathsf{|2x - 1| - 5}}_{zero}| = 0} \\\\ \mathsf{|2x - 1| - 5 = 0} \\\\ \mathsf{|2x - 1| = 5}$

Da definição de módulo,

$\\ \mathsf{|2x - 1| = \pm 5} \\\\ \mathsf{\Rightarrow \begin{cases} \mathsf{2x - 1 = + 5 \Rightarrow 2x = 6 \Rightarrow \boxed{\mathsf{x = 3}}} \\ \mathsf{2x - 1 = - 5 \Rightarrow 2x = - 4 \Rightarrow \boxed{\mathsf{x = - 2}}} \end{cases}}$

Answer 2

║2x-1 Ι -5 Ι = 0
  I 2x -1 I -5 = 0
  I 2X-1 I = 5
  2X-1 =5
  2X-1 = -5
  X=3
  X= - 2
  x₁ = - 2, x₂ = 3