Question

Giải pt:

|2x-6|=3x+1

Answer 1

\(\left|2x-6\right|=3x+1\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-6=3x+1\\6-2x=3x+1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-x=7\\-5x=-5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-7\\x=1\end{matrix}\right.\)

Vậy \(S=\left\{1;-7\right\}\)

Answer 2

Ta có: \(\left|2x-6\right|=3x+1\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-6=3x+1\left(x\ge3\right)\\2x-6=-3x-1\left(x< 3\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-x=7\\5x=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-7\left(loại\right)\\x=1\left(nhận\right)\end{matrix}\right.\)