Question

Resolva a equação |2x – 4 |= x – 1 {3,5/3} {6,3} {5/2, 3} {3, 3/5}

Answer 1

Condição de existência:

$\mathsf{x-1\ge0\implies~x\ge1}$

$\mathsf{|2x-4| = x - 1 } \\\mathsf{ \implies\begin{cases}2x-4=x-1\\2x-4=-(x-1)\end{cases}}$

$\mathsf{2x-4=x-1}\\\mathsf{2x-x=4-1}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{x=3}}}}}$

$\mathsf{2x-4=-(x-1)}\\\mathsf{2x-4=-x+1}\\\mathsf{2x+x=4+1}\\\mathsf{3x=5}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{x=\dfrac{5}{3}}}}}}$

$\boxed{\boxed{\boxed{\boxed{\mathsf{s=\{3,\dfrac{5}{3}\}}}}}}$

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{\maltese~~alternativa~a}}}}}$