![a)\; \; |x-1|+|1-2x|=2|x|\\\\x-1=0\; \; \to \; \; x_1=1\; ;\; \; 1-2x=0\; \; \to \; \; x_2=0,5\; ;\; \; x_3=0\\\\znaki\; (x-1):\quad ---(0)---(0,5)---(1)+++\\\\znaki\; (1-2x):\quad +++(0)+++(0,5)---(1)---\\\\znaki\; (x):\qquad ---(0)+++(0,5)+++(1)+++\\\\1)\; \; -\infty <x\leq 0:\; \; |x-1|=-(x-1)=1-x\; ,\; \; |1-2x|=1-2x\; ,\; \; |x|=-x\; ,\\\\|x-1|+|1-2x|=2|x|\; \; \to \; \; 1-x+1-2x=-2x\; ,\\\\2-3x=-2x\; ,\; \; x=2\notin (-\infty ,0\, ]\\\\2)\; \; 0<x\leq 0,5:\; \; |x-1|=1-x\; ,\; \; |1-2x|=1-2x\; ,\; \; |x|=x\; , a)\; \; |x-1|+|1-2x|=2|x|\\\\x-1=0\; \; \to \; \; x_1=1\; ;\; \; 1-2x=0\; \; \to \; \; x_2=0,5\; ;\; \; x_3=0\\\\znaki\; (x-1):\quad ---(0)---(0,5)---(1)+++\\\\znaki\; (1-2x):\quad +++(0)+++(0,5)---(1)---\\\\znaki\; (x):\qquad ---(0)+++(0,5)+++(1)+++\\\\1)\; \; -\infty <x\leq 0:\; \; |x-1|=-(x-1)=1-x\; ,\; \; |1-2x|=1-2x\; ,\; \; |x|=-x\; ,\\\\|x-1|+|1-2x|=2|x|\; \; \to \; \; 1-x+1-2x=-2x\; ,\\\\2-3x=-2x\; ,\; \; x=2\notin (-\infty ,0\, ]\\\\2)\; \; 0<x\leq 0,5:\; \; |x-1|=1-x\; ,\; \; |1-2x|=1-2x\; ,\; \; |x|=x\; ,](https://tex.z-dn.net/?f=a%29%5C%3B%20%5C%3B%20%7Cx-1%7C%2B%7C1-2x%7C%3D2%7Cx%7C%5C%5C%5C%5Cx-1%3D0%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20x_1%3D1%5C%3B%20%3B%5C%3B%20%5C%3B%201-2x%3D0%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20x_2%3D0%2C5%5C%3B%20%3B%5C%3B%20%5C%3B%20x_3%3D0%5C%5C%5C%5Cznaki%5C%3B%20%28x-1%29%3A%5Cquad%20---%280%29---%280%2C5%29---%281%29%2B%2B%2B%5C%5C%5C%5Cznaki%5C%3B%20%281-2x%29%3A%5Cquad%20%2B%2B%2B%280%29%2B%2B%2B%280%2C5%29---%281%29---%5C%5C%5C%5Cznaki%5C%3B%20%28x%29%3A%5Cqquad%20---%280%29%2B%2B%2B%280%2C5%29%2B%2B%2B%281%29%2B%2B%2B%5C%5C%5C%5C1%29%5C%3B%20%5C%3B%20-%5Cinfty%20%3Cx%5Cleq%200%3A%5C%3B%20%5C%3B%20%7Cx-1%7C%3D-%28x-1%29%3D1-x%5C%3B%20%2C%5C%3B%20%5C%3B%20%7C1-2x%7C%3D1-2x%5C%3B%20%2C%5C%3B%20%5C%3B%20%7Cx%7C%3D-x%5C%3B%20%2C%5C%5C%5C%5C%7Cx-1%7C%2B%7C1-2x%7C%3D2%7Cx%7C%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%201-x%2B1-2x%3D-2x%5C%3B%20%2C%5C%5C%5C%5C2-3x%3D-2x%5C%3B%20%2C%5C%3B%20%5C%3B%20x%3D2%5Cnotin%20%28-%5Cinfty%20%2C0%5C%2C%20%5D%5C%5C%5C%5C2%29%5C%3B%20%5C%3B%200%3Cx%5Cleq%200%2C5%3A%5C%3B%20%5C%3B%20%7Cx-1%7C%3D1-x%5C%3B%20%2C%5C%3B%20%5C%3B%20%7C1-2x%7C%3D1-2x%5C%3B%20%2C%5C%3B%20%5C%3B%20%7Cx%7C%3Dx%5C%3B%20%2C)
1:\; \; |x-1|=x-1\; ,\; \; |1-2x|=2x-1\; ,\; \; |x|=x\; ,\\\\x-1+2x-1=2x\; ,\; \; 3x-2=2x\; ,\; \; \underline {x=2\in (1,+\infty )}\\\\Otvet:\; \; x=0,4\; ,\; \; x=2\; ." alt="1-x+1-2x=2x\; ,\; \; 2-3x=2x\; ,\; \; 2=5x\; ,\; \; \underline {x=0,4\in (0\, ;\, 0,5\, ]}\\\\3)\; \; 0,51:\; \; |x-1|=x-1\; ,\; \; |1-2x|=2x-1\; ,\; \; |x|=x\; ,\\\\x-1+2x-1=2x\; ,\; \; 3x-2=2x\; ,\; \; \underline {x=2\in (1,+\infty )}\\\\Otvet:\; \; x=0,4\; ,\; \; x=2\; ." align="absmiddle" class="latex-formula">
![b)\; \; |x^2-5x+6|=-(x^2-5x+6)\; \; \Rightarrow \; \; \underline {x^2-5x+6<0}\\\\x^2-5x+6=0\; \; \to \; \; x_1=2\; ,\; x_2=3\; \; \; (teorema\; Vieta)\\\\x^2-5x+6=(x-2)(x-3)\\\\(x-2)(x-3)<0\\\\znaki:\; \; +++(2)---(3)+++\\\\x\in (2,3)\\\\\star \; \; |x|=\left \{ {{x\; ,\; esli\; x\geq 0\; ,} \atop {-x\; ,\; esli\; x<0\; .}} \right. b)\; \; |x^2-5x+6|=-(x^2-5x+6)\; \; \Rightarrow \; \; \underline {x^2-5x+6<0}\\\\x^2-5x+6=0\; \; \to \; \; x_1=2\; ,\; x_2=3\; \; \; (teorema\; Vieta)\\\\x^2-5x+6=(x-2)(x-3)\\\\(x-2)(x-3)<0\\\\znaki:\; \; +++(2)---(3)+++\\\\x\in (2,3)\\\\\star \; \; |x|=\left \{ {{x\; ,\; esli\; x\geq 0\; ,} \atop {-x\; ,\; esli\; x<0\; .}} \right.](https://tex.z-dn.net/?f=b%29%5C%3B%20%5C%3B%20%7Cx%5E2-5x%2B6%7C%3D-%28x%5E2-5x%2B6%29%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20%5Cunderline%20%7Bx%5E2-5x%2B6%3C0%7D%5C%5C%5C%5Cx%5E2-5x%2B6%3D0%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20x_1%3D2%5C%3B%20%2C%5C%3B%20x_2%3D3%5C%3B%20%5C%3B%20%5C%3B%20%28teorema%5C%3B%20Vieta%29%5C%5C%5C%5Cx%5E2-5x%2B6%3D%28x-2%29%28x-3%29%5C%5C%5C%5C%28x-2%29%28x-3%29%3C0%5C%5C%5C%5Cznaki%3A%5C%3B%20%5C%3B%20%2B%2B%2B%282%29---%283%29%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%282%2C3%29%5C%5C%5C%5C%5Cstar%20%5C%3B%20%5C%3B%20%7Cx%7C%3D%5Cleft%20%5C%7B%20%7B%7Bx%5C%3B%20%2C%5C%3B%20esli%5C%3B%20x%5Cgeq%200%5C%3B%20%2C%7D%20%5Catop%20%7B-x%5C%3B%20%2C%5C%3B%20esli%5C%3B%20x%3C0%5C%3B%20.%7D%7D%20%5Cright.)