Math 1 · Unit 5 · Lesson 4
Inequalities in the Real World
A real limit, such as spending at most $20 on $2 hot dogs and $3 drinks, is a constraint: 2x + 3y is at most 20. Its region is every combination you can afford. The boundary is the most you can buy; inside is under budget. When you can only buy whole things, only the whole-number points count. And when there are two limits, the answers are where the regions overlap.
The big idea
A real limit is a constraint, and a constraint is an inequality: the total, the sign, the limit. Its graph is every combination that obeys the rule, the feasible region. The boundary line is using the limit exactly, the most you can do; inside is under it. To ask whether a particular combination is allowed, find its point, or put the numbers in and read the sentence. Then ask the Unit 2 question: any amount, or whole things? For hot dogs and tickets only the whole-number points are real, so the answer is a set of dots inside the region. And when a story has two limits, both regions get shaded and the answers live in the overlap, which is where Unit 6 begins.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with constraints, feasible regions, reading answers, discrete versus continuous, the overlap preview, and a worked example. Plus a worksheet with grids and an answer key, and a short lesson plan.