Greater than, less than.
Solving equations where the answer is a range, not a point.
Essential for calculating risk and safety limits.
If you multiply/divide by a negative, FLIP the inequality sign!
In Plain English: Sometimes you don't need an exact number, you just need 'at least' or 'no more than'. An elevator limit isn't exactly 2000lbs, it's 'anything less than 2000lbs'.
In The Real World: Speed limits. Budgeting (spending LESS than you make).
Forgetting to flip the sign when dividing by a negative. -2x > 10 becomes x < -5.