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!
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'.
Real-world example: Speed limits. Budgeting (spending LESS than you make).
Forgetting to flip the sign when dividing by a negative. -2x > 10 becomes x < -5.