Question

/4-x/+2x=3

/ là trị tuyệt đối

Answer 1

\(\left|4-x\right|+2x=3\) \(\Rightarrow\) Có 2 trường hợp xảy ra:

TH1: \(4-x+2x=3\)

\(\Rightarrow4+x=3\)

\(\Rightarrow x=3-4=-1\)

TH2: \(-\left(4-x\right)+2x=3\)

\(\Rightarrow-4+x+2x=3\)

\(\Rightarrow-4+3x=3\)

\(\Rightarrow3x=3-4=-1\)

\(\Rightarrow x=-1:3=\dfrac{-1}{3}\)

Vậy \(x\in\left\{-1;\dfrac{-1}{3}\right\}\)

Answer 2

\(\left|4-x\right|+2x=3\)

TH1: \(4-x\ge0\Leftrightarrow x\le4\)

\(4-x+2x=3\\ \Leftrightarrow4+x=3\\ \Leftrightarrow x=3-4\\ \Leftrightarrow x=-1\left(TM\right)\)

TH2: \(4-x< 0\Leftrightarrow x>4\)

\(-\left(4-x\right)+2x=3\\ \Leftrightarrow-4+x+2x=3\\ \Leftrightarrow-4+3x=3\\ \Leftrightarrow3x=3+4\\ \Leftrightarrow3x=7\\ \Leftrightarrow x=\dfrac{7}{3}\left(KTM\right)\)

Vậy $x=-1$ là nghiệm phương trình