\(\Rightarrow\)2(n-7) - (2n+3) \(⋮\)2n+3
\(\Rightarrow\)(2n-14) - (2n+3) \(⋮\)2n+3
\(\Rightarrow\)2n - 14 - 2n - 3 \(⋮\)2n+3
\(\Rightarrow\)-17 \(⋮\)2n+3
\(\Rightarrow2n+3\inƯ\left(-17\right)=\left(1;-1;17;-17\right)\)
ta có bảng sau :
2n+3 1 -1 17 -17
n -1 -2 7 -10
mà \(n\in Z\)
\(\Rightarrow n\in\left(-1;-2;7;-10\right)\)
theo bài ra ta có:\
\(\left(n-7\right)⋮\left(2n+3\right)\)
=> (n - 7) - (2n+3) \(⋮2n+3\)
=> \(2\left(n-7\right)-\left(2n+3\right)⋮2n+3\)
=> \(2n-4-2n-3⋮2n+3\)
=> \(-7⋮2n+3\)
=> 2n+3 E Ư(-7) = { 1;-1;7;-7 }
ta có bảng sau:
| 2n+3 | 1 | -1 | 7 | -7 |
| 2n | -2 | -4 | 4 | -10 |
| n | -1 | -2 | 2 | -5 |
vậy n ={ -1;-2;2;-5 }
