Question

tìm số nguyên x biết (3x-2)chia hết cho (2x+1)

Answer 1

\(3x-2⋮2x+1\)

\(\Rightarrow2\left(3x-2\right)⋮2x+1\)

\(\Rightarrow6x-4⋮2x+1\)

\(\Rightarrow6x+3-7⋮2x+1\)

\(\Rightarrow3\left(2x+1\right)-7⋮2x+1\)

\(\Rightarrow7⋮2x+1\)

\(\Rightarrow2x+1\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

\(\Rightarrow\left[{}\begin{matrix}2x+1=1\\2x+1=-1\\2x+1=7\\2x+1=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=3\\x=-4\end{matrix}\right.\)