← all archetypes

Model with an Inequality, Then Read the Range

A situation with a threshold -- at least, cheaper than, before the deadline -- becomes a linear inequality in the unknown. The modelling is the same as for an equation; what changes is that the answer is an interval, so the boundary (included or not, rounded which way) decides it, and two thresholds on one situation give a range squeezed from both sides.

grade 7–8 ExpressionsGeometry Convert to AlgebraEliminate Possibilities

Builds on: Count One Quantity Two Ways and EquateInequality Range Membership

Progression (5)

g7 1. One win count sets both players' scores Expressions · foundational
g7 2. Moving-point triangle area by subtraction ExpressionsGeometry · foundational
g7 3. Average cost under a flat fee plus surcharge Expressions · core
g7 4. Spend downstream time first, bound upstream speed RatiosExpressions · core
g7 5. Two thresholds on one mixture give a range ExpressionsRatios · advanced