1. Any real number can be added to (or subtracted from) both sides of an inequality, producing a new inequality with the same direction as the original one.

2. Both sides of an inequality can be multiplied (or divided) by a positive number to produce a new inequality with the same direction as the original one.

3. Both sides of an inequality can be multiplied (or divided) by a negative number to produce a new inequality that has the opposite direction of the original one.