`2x+1` $\vdots$ `6-x` `(x` `\ne` `6)`
`=>2x+1` $\vdots$ `-(x-6)`
`=>2x+1` $\vdots$ `x-6`
`=>2x-12+12+1` $\vdots$ `x-6`
`=>2(x-6)+13` $\vdots$ `x-6`
Vì `x-6` $\vdots$ `x-6`
`=>2(x-6)` $\vdots$ `x-6`
Để `2(x-6)+13` $\vdots$ `x-6`
`=>13` $\vdots$ `x-6`
`=>x-6∈Ư(13)={1;13;-1;-13}`
Ta có bảng sau:
\begin{array}{|c|c|}\hline \text{x-6}&\text{1}&\text{13}&\text{-1}&\text{-13}\\\hline \text{x}&\text{7}&\text{19}&\text{5}&\text{-7}\\\hline\end{array}
Vậy `x∈{7;19;5;-7}`
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