or example: 15 > 3 ( fifteen is greater than 3 ) right ?
if you multiply or divide 15 by any negative number, it'll become a negative number.
for example, let's divide 15 and 3 by -3.
15 divided by -3 = -5 ( negative five)
3 divided by -3 = -1 ( negative one)
now here's the point, which one is greater? -5 or -1 ?
-1 is greater than -5, so you flip the sign, once was 15 > 3 and now -5 < -1
why did we flip the sign ? because we kept the numbers in the same place,
if you move -1 to the left then you wouldnt flip the sign, -1 > -5.
the important thing is to keep the inequality true, that's why flipping the sign is important. if you keep the numbers in the same place, flip the sign, if you dont wanna flip the sign, move the numbers to the opposite side and keep the sign.