Home/Integrated Math 1/Lesson 76

Write two-variable inequalities: word problems

Convert constraints from context into two-variable inequalities.

Do this: Read the concept below, then try the quiz or activity.

Lesson 76 of 192
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Concept

Objective: Students will model real constraints using two-variable linear inequalities.

Estimated Time: 12 minutes

Standards:
HSA-CED.A.1HSA-CED.A.3

Identify quantities, define variables, and translate phrases like “at most,” “at least,” and “no more than” into symbols.

Try it

Tickets cost $8 for students and $12 for adults. Revenue must be at least $240. Write an inequality.

Concept Check

“At most 50 total” translates to:

Concept Check

“At least” corresponds to:

Common Misconception
Always verify your result in context instead of trusting a first pass.

Modeling inequality steps

These steps are out of order — can you fix them?

1.Interpret and check units
2.Define variables
3.Translate each phrase
4.Combine into inequality

Short Answer

Why should variable definitions include units?

Mastery Check

Pass this check with at least 80% to unlock completion.

Question 1

“At most 50 total” translates to:

Question 2

“At least” corresponds to:

Pass the mastery check (80%+) to unlock completion.