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MathidiaMathematics Academy
Simultaneous equations and inequalities
Lesson 28 of 75
Standard practice

Inequality regions

Objective. Model feasible regions from several linear constraints.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Inequality regions is developed here as connected GCSE mathematics, not a memorised shortcut. Solve demanding linked systems algebraically and graphically. The lesson moves from a precise representation and key definitions to fluent procedure, linked reasoning and an unfamiliar application. Learners compare possible methods, state restrictions and assumptions, preserve exact values where appropriate, and justify accuracy, notation and units before evaluating whether the result is mathematically and contextually reasonable.

Worked example

Why might an algebraic solution be rejected in context?

it may violate a stated c…
Illustrated card showing it may violate a stated constraint
  1. 1Translate the information into a labelled diagram, table, graph or algebraic statement and identify every constraint.
  2. 2Select the most efficient GCSE method, explain why its conditions apply, and keep exact values until approximation is requested.
  3. 3Carry out each transformation on a separate justified line, tracking signs, units, domains and required accuracy.
  4. 4Verify with substitution, an inverse method, estimation or a second representation. The checked result is it may violate a stated constraint.

Answer: it may violate a stated constraint

Concept mastery

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. A common error in inequality regions is applying a familiar rule before checking its conditions, domain or direction. Name the structure first, retain exact values, and test the final result against every original constraint.

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