Why does the inequality sign change when both sides are multiplied or divided by a negative number?

Let's look at two points on the number line, say 2 and 3. Now 2 is 2 units from 0 and 3 is 3 units away from 0 If you multiply by a negative 1, then 2 become -2 and 3 become -3. So they are the same distance from 0 but their positions changes to the opposite side of zero. In general given points A, B on the number line, multiplying by negative one will preserve the distance which is know as the absolute value but move the points to the other side of 0. Now multiplying by a negative number other than one does the same thing but the absolute value is multiplied by the number as well. For example, 2 x-3 is -6. We multiplied the distance form 0 which was 2 by 3 and changed the position. This is called a reflection. So now picture a vertical line, perhaps right down the middle of this page. If I put two point A and B on the right side of the line and put A closer to the line which I will all zero, and B farther, then A