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.

Core Idea

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

Understanding

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."

Step by Step

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.

Misconceptions

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.

Question

Worked Example

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?

Select an answer to see the explanation