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