Algebra / Linear Inequalities
Context-based inequality constraints
Words such as at most, at least, minimum, maximum, and budget indicate inequality direction. Integer contexts may require rounding up or down.
Least you need to know
- At most means $\le$.
- At least means $\ge$.
- A greatest whole number under a limit is found by rounding down.
Key notation
- m — A context variable, such as miles or minutes
Worked example
A $6 fee plus $2 per item with at most $20 available gives $6+2x\le 20$, so $x\le 7$.
Common mistakes
- Rounding must preserve the context.
- The setup fee should be included before solving.
How to recognize it
- The stem includes a budget, capacity, minimum, or greatest/least whole number.
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