Modeling Constraints

Learn and apply modeling constraints using equations, examples, and interpretation.

Lesson 5 of 53 parts Practice Flashcards

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Nonnegative Quantities

Objective: Explain and use nonnegative quantities in an Algebra 1 problem.

Counts, elapsed times, and distances often require nonnegative domains, even if a symbolic inequality permits negative numbers. It determines which algebraic values are meaningful.

Worked examples

Try itExample 1.1: A maximum of 23 items can be carried. If 13 are already packed, what is the largest additional number?Show answer

10. Subtract the 13 items already packed from capacity. The answer is 10.

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Nonnegative Quantities

Objective: Explain and use nonnegative quantities in an Algebra 1 problem.

Counts, elapsed times, and distances often require nonnegative domains, even if a symbolic inequality permits negative numbers. It determines which algebraic values are meaningful.

Worked examples

Try itExample 1.1: A maximum of 23 items can be carried. If 13 are already packed, what is the largest additional number?Show answer

10. Subtract the 13 items already packed from capacity. The answer is 10.

Capacity Bounds

Objective: Explain and use capacity bounds in an Algebra 1 problem.

At most corresponds to ≤ and at least to ≥; translate the limit together with known starting amounts. Less than or equal to.

Worked examples

Try itExample 2.1: A maximum of 47 items can be carried. If 23 are already packed, what is the largest additional number?Show answer

24. Subtract the 23 items already packed from capacity. The answer is 24.

Integer Solutions

Objective: Explain and use integer solutions in an Algebra 1 problem.

Whole items require integer solutions, so the largest feasible count may be the greatest integer below a real-number bound. Rounding up would exceed the bound.

Worked examples

Try itExample 3.1: A maximum of 77 items can be carried. If 33 are already packed, what is the largest additional number?Show answer

44. Subtract the 33 items already packed from capacity. The answer is 44.

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