Ta có: $5x+13\vdots 2x+1$
$⇒2.(5x+13)\vdots 2x+1$
$⇒10x+26\vdots 2x+1$
$⇒5.(2x+1)+21\vdots 2x+1$
VÌ: $5.(2x+1)\vdots 2x+1$
$⇒21\vdots 2x+1$
$⇒2x+1∈Ư(21)=${$±1;±3;±7;±21$}
Ta có bảng sau:
2x+1 1 -1 3 -3 7 -7 21 -21
2x 0 -2 2 -4 6 -8 20 -22
x 0 -1 1 -2 3 -4 10 -11
Vậy x∈{0;-1;1;-2;3;-4;10;-11}