CurriculumGrade 9Mathematics

Constraints and Viable Solutions

Aligned to A-CED.A.3 — Common Core State Standards for Mathematics.

What this lesson teaches

Real problems often have limits (constraints) written as equations or inequalities. A solution is viable only if it satisfies every constraint and makes sense in context.

Worked example

You have $50 for notebooks ($4 each) and pens ($1 each). The constraint is 4n + p ≤ 50 with n ≥ 0 and p ≥ 0. Buying n = 10, p = 5 costs 4(10) + 5 = 45 ≤ 50, so it is viable.

Practice questions

  1. Write a constraint for buying x shirts at $12 and y hats at $8 with a $100 budget.
  2. Is x = 6 shirts, y = 4 hats viable for that $100 budget? Show your check.
  3. Why must the number of shirts be a whole number that is 0 or more?

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Restricciones y Soluciones Viables

Los problemas reales suelen tener límites (restricciones) escritos como ecuaciones o desigualdades. Una solución es viable solo si cumple todas las restricciones y tiene sentido en el contexto.

Ejemplo: Tienes $50 para cuadernos ($4 cada uno) y plumas ($1 cada una). La restricción es 4n + p ≤ 50 con n ≥ 0 y p ≥ 0. Comprar n = 10, p = 5 cuesta 4(10) + 5 = 45 ≤ 50, así que es viable.

More Algebra lessons

Solving Linear Equations and InequalitiesA-REI.B.3Solving Quadratic Equations by FactoringA-REI.B.4Parts of an ExpressionA-SSE.A.1Rewriting by StructureA-SSE.A.2Equivalent Forms of ExpressionsA-SSE.B.3Operations with PolynomialsA-APR.A.1

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