Question

|x - 2| = 3x + 2

Answer 1

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

\(\Leftrightarrow\left[{}\begin{matrix}x-2=3x+2\\x-2=-\left(3x+2\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=0\end{matrix}\right.\)

Answer 2

\(\left|x-2\right|=3x+2\\\Leftrightarrow \left[{}\begin{matrix}x-2=3x+2\\-\left(x-2\right)=3x+2\end{matrix}\right.\\\Leftrightarrow\left[{}\begin{matrix}-2x=4\\-4x=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=0\end{matrix}\right. \)

Answer 3

\(\left|x-2\right|=3x+2\left(1\right)\)

*) Nếu \(x-2\ge0\)

\(\Leftrightarrow x\ge2\)

PT \(\left(1\right)\) có : \(x-2=3x+2\)

\(\Leftrightarrow x=-2\)( Ko thỏa mãn )

*) Nếu \(x-2< 0\)

\(\Leftrightarrow x< 2\)

PT \(\left(1\right)\)có : \(x-2=-3x-2\)

\(\Leftrightarrow x=0\)( Thỏa mãn)

Vậy pt có 1 nghiệm duy nhất là \(x=0\)

Answer 4

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

<=> \(\left[{}\begin{matrix}x-2=3x+2\left(x\ge2\right)\\2-x=3x+2\left(x< 2\right)\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}2x=-4\left(x\ge2\right)\\4x=0\left(x< 2\right)\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=-2\left(x\ge2\right)\left(loại\right)\\x=0\left(x< 2\right)\left(tm\right)\end{matrix}\right.\) 

Vậy nghiệm của phương trình trên là \(S=\left\{0\right\}\)

Chúc bạn học tốt

Answer 5

Ta có: \(\left|x-2\right|=3x+2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=3x+2\left(x\ge2\right)\\-x+2=3x+2\left(x< 2\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3x=2+2\\-x-3x=2-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-2x=4\\-4x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\left(loại\right)\\x=0\left(nhận\right)\end{matrix}\right.\)

Vậy: S={0}