Question

|x-|x-|x-1|||=0.5
| это скобка модуля

Answer 1

$\Big|\, x-\, |\, x-|x-1|\, |\Big|=0,5\ \ \ \Rightarrow \ \ \ \ \ x-|\, x-|\, x-1|\, |=\pm 0,5\\\\\\1)\ \ x-|\, x-|\, x-1|\, |=-0,5\ \ \ \to \ \ \ \ \ |x-|\, x-1|\, |=x+0,5\ \ \ \Rightarrow \\\\a_1)\ x-|\, x-1|=-(x+0,5)\ \ ,\ \ x-|\, x-1|=-x-0,5\ \ \ \to \\\\\ |x-1|=2x+0,5\ \ \ \Rightarrow \ \ \ x-1=\left[\begin{array}{ccc}2x+0,5\ \ ,\ esli\ x\geq 1\ ,\\-2x-0,5\ \ ,\ esli\ x<1\ .\end{array}\right\\\\\\\star \ \ x\geq 1:\ x-1=2x+0,5\ \ ,\ \ x=-1,5<1\ \ \to \ \ x\in \varnothing$

$\star \star \ \ x<1:\ \ x-1=-2x-0,5\ \ ,\ \ 3x=0,5\ \ ,\ \ \underline {\ x=\dfrac{1}{6}<1\ }$

$a_2)\ \ x-|x-1|=x+0,5\ \ \ \to \ \ \ |x-1|=-0,5<0\ \ \ \Rightarrow \ \ x\in \varnothing \\\\\\2)\ \ x-|\, x-|x-1|\, |=0,5\ \ \ \to \ \ \ |x-|\, x-1|\, |=x-0,5\ \ \Rightarrow \\\\x-|x-1|=\pm (x-0,5)\\\\a_3)\ \ x-|x-1|=-(x-0,5)\ \ \ \to \ \ \ x-|x-1|=-x+0,5\ \ ,\\\\|x-1|=2x-0,5\ \ \ \Rightarrow \ \ \ x-1=\left[\begin{array}{ccc}2x-0,5\ ,\ esli\ x\geq 0,25\ ,\\-2x+0,5\ ,\ esli\ x<0,25\ .\end{array}\right\\\\\star \ \ x\geq 0,25:\ x-1=2x-0,5\ \ ,\ \ x=-0,5<0,25\ \ \to \ \ x\in \varnothing$

$\star \star \ \ x<0,25:\ \ x-1=-2x+0,5\ \ ,\ \ 3x=1,5\ \ ,\ \ \underline {x=\dfrac{1}{6}<0,25\ }$

$a_4)\ \ x-|x-1|=x-0,5\ \ \to \ \ \ |x-1|=0,5\ \ ,\\\\x-1=\pm 0,5\\\\x-1=0,5\ \ \to \ \ \ \underline {\ x=1,5\ }\\\\x-1=-0,5\ \ \to \ \ \ \underline{\ x=0,5\ }\\\\\\Otvet:\ \ x=\dfrac{1}{6}\approx 0,17\ \ ,\ \ x=0,5\ \ ,\ \ x=1,5\ .$

График смотри на рисунке .