Question

Comparação de funções com modulo ,
por favor ajudem
|4x-2|=|2-1|

Answer 1

$4x-2 \geq 0---\ \textgreater \ 4x \geq 2---\ \textgreater \ x \geq \frac{1}{2} \\ |4x-2|=4x-2 \\ \\ \\ 4x-2\ \textless \ 0---\ \textgreater \ x\ \textless \ \frac{1}{2} \\ |4x-2|=-(4x-2) \\ \\ \\ 2-1 \geq 0--\ \textgreater \ 2 \geq 1$ verdadeiro
$|2-1|=2-1 \\ \\ \\ 2-1\ \textless \ 0---\ \textgreater \ 2\ \textless \ 1$ falso
$|2-1|=-(2-1)$

$x\ \textless \ \frac{1}{2}$

$(-4(4x-2))=(2-1) \\ \\ -4x+2=2-1 \\ \\ -4x=-1 \\ \\ x= \frac{1}{4}$

$x \geq \frac{1}{2} \\ \\ (4x-2)=(2-1) \\ \\ 4x=2+2-1 \\ \\ x= \frac{3}{4}$

Para 

$x\ \textless \ \frac{1}{2} ---\ \textgreater \ x= \frac{1}{4}$

Para

$x \geq \frac{1}{2} ---\ \textgreater \ x= \frac{3}{4}$

Resposta

$x= \frac{1}{4} ou x= \frac{3}{4}$