Translate constraints from context into inequalities and interpret feasible solutions. | Linear inequalities in one or two variables | SAT Math

Translate real-world limits into inequalities and interpret the feasible solution set.

核心知识

Identify the quantities, write an inequality that captures the constraint (budget, capacity, minimum requirement), and interpret the solution in context.

深入理解

SAT word problems often describe limits: a budget you can't exceed, a minimum number of hours, a maximum weight. Your job is to turn that language into a mathematical inequality.

Key translations: "at most" or "no more than" → $\leq$ . "At least" or "no fewer than" → $\geq$ . "More than" → $>$ . "Less than" → $<$ .

Once you write the inequality, solve or simplify it. Then interpret the answer in the original context — the SAT frequently asks what the solution means, not just what it is. A solution like $𝑥 \leq 15$ might mean "the store can buy at most 15 cases."

分步讲解

Define variables for the unknown quantities.
Identify the constraint language (at most, at least, no more than, etc.) and translate it into an inequality symbol.
Build the inequality using the given rates, costs, or quantities.
Solve the inequality and state the answer in the context of the problem.

常见误解

Confusing "at most" (≤) with "at least" (≥) — read the constraint direction carefully.
Writing an equation instead of an inequality when the problem says "no more than" or "up to."
Forgetting to interpret the solution in context — the SAT often asks what the number means, not just its value.

题目

示例解析

A shipping container can hold at most 1,200 pounds. Each large box weighs 60 pounds and each small box weighs 25 pounds. If $𝑙$ large boxes and $𝑠$ small boxes are loaded, which inequality models this constraint?

选择一个答案查看解析