Algebra / Linear Inequalities
Constraints from context
Context problems often translate into equations or inequalities by tracking units. Totals, budgets, minimums, and maximums determine the operation and inequality direction.
Least you need to know
- At least means $\ge$.
- At most means $\le$.
- Fixed plus variable cost is often modeled as $b+rx$.
Key notation
- \le — Less than or equal to, often used for an upper limit
- \ge — Greater than or equal to, often used for a minimum
Worked example
A $5 fee plus $3 per item with a budget of $50 is $5+3x\le 50$.
Common mistakes
- Do not swap fixed and per-unit quantities.
- Keep counts and dollars in separate equations.
How to recognize it
- The stem includes words such as at least, at most, total, budget, fee, or per.
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