知识点 3
Translate real-world constraints into equations or inequalities and interpret feasibility.
核心知识
A context usually gives both a calculation rule and a limit. Translate both, then check whether the result is actually possible in the real situation.
深入理解
Translate both layers. One expression or equation models the quantity, and a separate limit tells you what is allowed.
Words like at most, at least, and no fewer than create constraints, not just calculations. After you solve, check whether the result is actually feasible in context.
- Define the variable with its unit or meaning.
- Translate the main rule.
- Translate the limit words into an inequality.
- Reject answers that are algebraically valid but impossible in context.
分步讲解
- Define the variable with its unit or meaning.
- Translate the cost or quantity rule into an expression or equation.
- Translate limit words such as at least or at most into inequalities.
- Check whether the candidate answer satisfies every condition in the context.
常见误解
- Using an equation when the wording creates an inequality.
- Forgetting a fixed fee, minimum requirement, or maximum limit.
- Accepting a value that works algebraically but is not feasible in context.
题目
示例解析
A club is ordering custom T-shirts. The printer charges a one-time setup fee of
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