Divide by a Positive

3x < 12: three copies of x add up to less than 12, so one copy is less than 4. Dividing both sides by 3 says exactly that:

3x ÷ 3 < 12 ÷ 3

x < 4

Dividing both sides by a positive number keeps the sign as it is. If 6 < 12, then 2 < 4: halving both keeps the order.

So far, then, every move behaves like it did for equations: add, subtract, divide by a positive number, and the sign looks after itself. One move will turn out to be different, and it gets its own lesson.