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 examples
Example 1
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.
Example 2
A truck holds 2,000 lb. With crates at 80 lb and boxes at 15 lb: 80c + 15b ≤ 2000, c ≥ 0, b ≥ 0, both whole numbers.
Example 3
The integer requirement matters. 4.7 crates solves the inequality and cannot be loaded.
Practice questions
- Write a constraint for buying x shirts at $12 and y hats at $8 with a $100 budget.
- Is x = 6 shirts, y = 4 hats viable for that $100 budget? Show your check.
- 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.
▶ Watch this lessonEn 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 1: 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.
Ejemplo 2: Un camión soporta 2,000 lb. Con huacales de 80 lb y cajas de 15 lb: 80h + 15c ≤ 2000, h ≥ 0, c ≥ 0, los dos enteros.
Ejemplo 3: El requisito de números enteros importa. 4.7 huacales cumple la desigualdad y no se puede cargar.
More Algebra lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required