Question

Cum se rezolva |2x-1|-2*|1-x|=x? Vă rog dați-mi raspunsul cat mai repede!!!

Answer 1

$|2x-1|-2*|1-x|=x$
$|2x-1|-2*|1-x|-x=0$
$2x-1-2(1-x)-x=0, 2x-1 \geq 0, 1-x \geq 0$
$-(2x-1)-2(1-x)-x=0, 2x-1\ \textless \ 0, 1-x \geq 0$
$2x-1-2x(-(1-x))-x=0, 2x-1 \geq 0, 1-x\ \textless \ 0$
$-(2x-1)-2*(-(1x))-x=0, 2x-1\ \textless \ 0, 1-x\ \textless \ 0$
$x=1, x \geq \frac{1}{2}, x \leq 1$
$x=-1, x\ \textless \ \frac{1}{2}, x \leq 1$
$x=1, x \geq \frac{1}{2}, x\ \textgreater \ 1$
$x= \frac{3}{5},x\ \textless \ \frac{1}{2}, x\ \textgreater \ 1$
x=1, x∈$[ \frac{1}{2},1]$
x=-1 x∈(-∞,$\frac{1}{2})$
x=1, x∈(1,+∞)
$x= \frac{3}{5}$, x∈∅
x=1
x=-1
x∈∅
x∈∅
x=-1
x=1