Câu hỏi của Quynh Chi

Question

|2x-3|+|x-1|=1

ngonhuminh · Accepted Answer

$\left|2x-3\right|+\left|x-1\right|=1$

$\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 1\3-2x+1-x=1\Rightarrow3x=3\Rightarrow x=1\left(l\right)\end{matrix}\right.\\left\{{}\begin{matrix}1\le x< \dfrac{3}{2}\3-2x+x-1=1\Rightarrow x=1\left(n\right)\end{matrix}\right.\\left\{{}\begin{matrix}x\ge\dfrac{3}{2}\2x-3+x-1=1\Leftrightarrow3x=5;x=\dfrac{5}{3}\left(n\right)\end{matrix}\right.\end{matrix}\right.$Câu trả lời: $\left|2x-3\right|+\left|x-1\right|=1$

$\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 1\3-2x+1-x=1\Rightarrow3x=3\Rightarrow x=1\left(l\right)\end{matrix}\right.\\left\{{}\begin{matrix}1\le x< \dfrac{3}{2}\3-2x+x-1=1\Rightarrow x=1\left(n\right)\end{matrix}\right.\\left\{{}\begin{matrix}x\ge\dfrac{3}{2}\2x-3+x-1=1\Leftrightarrow3x=5;x=\dfrac{5}{3}\left(n\right)\end{matrix}\right.\end{matrix}\right.$

nguyen thi vang · Answer

Lập bảng xét dấu : x 2x-3 x-1 1 3 2 - 0 - + 0 - + + *TH1 : x < 1 => $-2x+3-x+1=1$ $\Leftrightarrow-3x+4=1$ $\Leftrightarrow-3x=-3$ $\Leftrightarrow x=1$ (loại) * TH2 : $1\le x< \dfrac{3}{2}$$\Rightarrow-2x+3+x-1=1$ $\Leftrightarrow-x+2=1$ $\Leftrightarrow x=1$ (TM) * TH3 : $x\ge\dfrac{3}{2}$ $\Rightarrow2x-3+x-1=1$ $\Leftrightarrow3x-4=1$ $\Leftrightarrow3x=5$ $\Leftrightarrow x=\dfrac{5}{3}\left(TM\right)$Câu trả lời: Lập bảng xét dấu : x 2x-3 x-1 1 3 2 - 0 - + 0 - + + *TH1 : x < 1 => $-2x+3-x+1=1$ $\Leftrightarrow-3x+4=1$ $\Leftrightarrow-3x=-3$ $\Leftrightarrow x=1$ (loại) * TH2 : $1\le x< \dfrac{3}{2}$$\Rightarrow-2x+3+x-1=1$ $\Leftrightarrow-x+2=1$ $\Leftrightarrow x=1$ (TM) * TH3 : $x\ge\dfrac{3}{2}$ $\Rightarrow2x-3+x-1=1$ $\Leftrightarrow3x-4=1$ $\Leftrightarrow3x=5$ $\Leftrightarrow x=\dfrac{5}{3}\left(TM\right)$

Bài 5: Phương trình chứa dấu giá trị tuyệt đối

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