Inequality Word Problems

Key Phrases for Inequalities

| Phrase | Symbol | |--------|--------| | "at least", "minimum", "no less than" | $\geq$ | | "at most", "maximum", "no more than" | $\leq$ | | "more than", "greater than" | $>$ | | "less than", "fewer than" | $<$ |

Strategy

1. Define a variable
2. Write an inequality from the problem
3. Solve the inequality
4. Check if the answer makes sense in context

Common Scenarios

Budget problems: Total cost ≤ available money

Grade problems: Average score ≥ desired grade

Capacity problems: Number of people ≤ maximum capacity

Interpreting Solutions

Remember to consider realistic constraints:

• Can't have negative people
• Can't work negative hours
• Round to whole numbers when appropriate