Ta có: \(2x+1=2\left(x-3\right)+7\)
Vì \(2\left(x-3\right)⋮\left(x-3\right)\Rightarrow7⋮\left(x-3\right)\)
\(\Rightarrow x-3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
Nếu x - 3 = 1 thì x = 4
Nếu x - 3 = -1 thì x = 2
Nếu x - 3 = 7 thì x = 10
Nếu x - 3 = -7 thì x = -4
Vậy \(x=\left\{4;-4;2;10\right\}\)