có x + 7 chia hết cho 2x – 7
=>2x+14$\vdots$2x-7
=>2x-7+21 $\vdots$ 2x-7
mà 2x-7 $\vdots$ 2x-7
=>21 $\vdots$ 2x-7
=>2x-7∈Ư(21)
mà Ư(21)={±1;±3;±7;±21}
=>2x-7∈{±1;±3;±7;±21}
kẻ bảng
2x-7 1 -1 3 -3 7 -7 21 -21
x 4 -3 5 -2 7 0 14 -7
=>x∈{-7;-3;-2;0;4;5;7;14}
vậy x∈{-7;-3;-2;0;4;5;7;14}